In other words, what thoughts regarding freedoms and rights from the
founders of a nation support a leader taking supreme power over its
Congress?
Generally speaking, one doesn't take "supreme power over Congress", one instead, disregards laws duly enacted by Congress or express mandates of the Constitution, including those related to cooperation with Congress.
The most notable recognized deviations from Congressional direction that are recognized (at least by some people) are:
The authority of the President to direct the military as commander-in-chief, and to a lesser extent, to conduct foreign policy. U.S. Constitution, Article II, Section 2. This power is balanced with the power of Congress to declare war and regulate the military via the War Powers Resolution of 1973 which has never really been tested in a "when push comes to shove" kind of way so far. The War Powers Resolution (a.k.a. the War Powers Act) requires the President to seek Congressional approval for new conflicts that arise that could become wars and predominantly Presidents have done so without necessarily acknowledging that they are obligated in a constitutionally valid way to do so.
The closely related power to unilaterally employ military force to ensure a Republican form of government or to respond to an invasion or insurrection or at the request of a governor, "domestic violence" without Congressional authorization. U.S. Constitution, Article IV, Section 4.
The United States shall guarantee to every state in this union a
republican form of government, and shall protect each of them against
invasion; and on application of the legislature, or of the executive
(when the legislature cannot be convened) against domestic violence.
Related to this is the power to suspend the writ of habeas corpus. U.S. Constitution, Article I, Section 9:
The privilege of the writ of habeas corpus shall not be suspended,
unless when in cases of rebellion or invasion the public safety may
require it.
In practice, however, this theoretically unilateral power of the President has never been very meaningful, because no President has ever sought to invoke it in circumstances in which he didn't already have solid and prompt legislative support from Congress.
For example, the suspension of habeas corpus by President Lincoln during the U.S. Civil War was backed by legislation from Congress, the Habeas Corpus Suspension Act of 1863.
But, the emergency power to limit the right of habeas corpus has been significantly restricted by U.S. Supreme Court case law:
In ex parte Milligan, the United States Supreme Court held that the
Habeas Corpus Suspension Act [of 1863] did not authorize military
tribunals, that as a matter of constitutional law the suspension of
habeas corpus did not itself authorize trial by military tribunals,
and that neither the Act nor the laws of war permitted the imposition
of martial law where civilian courts were open and operating
unimpeded.
The emergency powers of the President to use the military domestically are also limited by the Posse Comitatus Act and related legislation, which prohibits the use of the military to enforce civilian laws domestically in most circumstances, absent an invasion or insurrection.
The authority to pardon someone who has violated the law. U.S. Constitution, Article II, Section 2.
The authority to veto legislation subject to Congressional override. U.S. Constitution, Article I, Section 7.
The authority to not spend all funds that are authorized by Congress for a purposes that are not entitlements. This is implied in case law subject to limitations in a 1974 Act of Congress. This is called "impoundment of appropriated funds." But, one of the strongest limitations on Presidential power is that the President may not spend any money not appropriated by law by Congress. The President can constitutionally spend less than is appropriated by Congress, subject to the Impoundment Act of 1974, but not more. Since the Constitution prohibits many kinds of long term binding contracts and prospective appropriations that would bind future Congresses (except for the Naval contracts), see U.S. Constitution, Article I, this leaves the President on a fairly short leash and fairly accountable to Congress.
The authority to exercise discretion in not fully enforcing all violations of the law. This is implied in case law, especially, the law of prosecutorial discretion. The prosecutor's broad discretion in such areas as initiating or foregoing prosecutions, selecting or recommending specific charges, and terminating prosecutions by accepting guilty pleas has been recognized on numerous occasions by the courts. See, e.g., United States v. LaBonte, 520 U.S. 751, 762 (1997); Oyler v. Boles, 368 U.S. 448 (1962); United States v. Fokker Services B.V., 818 F.3d 733, 741 (D.C. Cir. 2016); Newman v. United States, 382 F.2d 479 (D.C. Cir. 1967); Powell v. Ratzenbach, 359 F.2d 234 (D.C. Cir. 1965). This discretion exists by virtue of the prosecutor's status as a member of the Executive Branch, and the President's responsibility under the Constitution to ensure that the laws of the United States be "faithfully executed." U.S. Constitution, Article II § 3. See Nader v. Saxbe, 497 F.2d 676, 679 n. 18 (D.C. Cir. 1974). Complete executive branch control of prosecutorial discretion, however, has been limited by the creation of independent agencies within the federal government and by the enactment of laws authorizing the appointment of a special prosecutor, like Robert Mueller, in cases where there is a risk of a conflict of interest from the President.
The authority to refrain from enforcing laws determined to be unconstitutional when that determination is not contrary to the controlling judicial branch ruling. This is implied in case law and in the duty to faithfully execute the constitution. U.S. Constitution, Article II, Section 1. This is closely related to prosecutorial discretion.
Sovereign immunity as applied to executive branch officials including the President, is mostly a product of case law although it has some statutory acknowledgement in relatively pedestrian claims like lawsuits for ordinary tort liability against the United States seeking money damages which must usually be brought in the U.S. Court of Claims, if they are allowed at all (with an important exception established in the Bivens case).
Case law has also recognized an "executive privilege" against forced disclosure of certain information by the executive branch although the scope of this privilege, which arises only from case law, is disputed. Only a handful of cases have addressed this, the most famous of which is United States v. Nixon discussed at the link.
There is also an unanswered question regarding when, if ever, a President's actions are clear and intentional violations of the law, and yet still might not constitute impeachable offenses set forth in U.S. Constitution, Article II, Section 4, or what remedies are available when an impeachable offense is committed but Congress is unwilling or unable (perhaps due to Presidential action) to conduct impeachment proceedings.
Other than these circumstances, the U.S. Constitution does not contemplate that the President has emergency powers of any kind. There are few precedents in which the President has defied the law and the will of Congress more generally based upon a claim of emergency powers.
The emergency powers of the President, in particular, and government, in general, are qualitatively and quantitatively, different from emergency powers in most other countries, which are, generally speaking, more expansive and have more formal recognition in the governing documents and laws of the countries in question.
For example, while a bipartisan coalition in the U.K. suspended elections during World War II, the United States has never, ever, under any circumstances suspended an election (except during the U.S. Civil War in the Confederate States, where the Confederacy that was the de facto regime there held its own elections instead).
Specific Legislation
Despite its name, the National Emergencies Act of 1976, doesn't really address the question.
Analytically, this is just a law authorizing the President to do certain things under certain circumstances, just like any other law, and not a law that gives the President "supreme power over Congress".
It is more like the laws governing disaster relief, which authorize the President, subject to specific criteria, to determine that a situation is a national disaster, upon which determination certain federal assistance is authorized.
This is why, even though scores of "emergencies" have been declared, many of which are still in force, they don't feel, to the general public, like "emergencies."
To the extent that the National Emergencies Act purports to go further, in ways not expressly authorized by the U.S. Constitution, it is an unconstitutional violation of the non-delegation doctrine and isn't a valid law. So, for example, Congress cannot delegate all of its law making power to the President via regulations. The Supreme Court ruled in J. W. Hampton, Jr. & Co. v. United States (1928) that:
"In determining what Congress may do in seeking assistance from
another branch, the extent and character of that assistance must be
fixed according to common sense and the inherent necessities of the
government co-ordination." So long as Congress "shall lay down by
legislative act an intelligible principle to which the person or body
authorized to [exercise the delegated authority] is directed to
conform, such legislative action is not a forbidden delegation of
legislative power."
For example, Congress is not constitutionally permitted to give the President line item veto power. Clinton v. City of New York (U.S. 1996).
Isn't the executive branch supposed to just execute? I.e. Execute the
bills proposed by the party he represents, as supported by that
party's allies?
The Executive branch is supposed to "execute" although it has considerable discretion in how it does so and has some express instances of unilateral power like the veto power and the pardon power.
But, the Executive branch is supposed to "execute" the laws enacted by Congress, not "the bills proposed by the party he represents, as supported by that party's allies."
From a legal and constitutional perspective, until a bill is passed by Congress and duly enacted as a law, the Executive branch not only can, but must, ignore them, in any capacity other than as one more lobbyist before Congress among others, on a hypothetically equal footing as everyone else (except that the President has the veto power and the VP can cast tie votes in the Senate, per Article I of the U.S. Constitution).
