What happens if Congress declares war, but POTUS refuses to fight it?

Question

By Article I, Section 8, Clause 11 of the US Constitution, the power to declare war is with the Congress.

Today (03/20/17), during a committee hearing, Ms. Speier, accused Russia (I assume she meant the Russian Federation) of having committed an act of war against The United States. If she introduces a resolution to declare war on the Russian Federation and convinces enough of her Republican colleagues to join her in voting for this resolution, and (because he has too many "Russian ties") President Trump refuses to execute the war, does that become an act of treason on his part?

Is he required to act on such a resolution? If he doesn't, is there any recourse other than impeachment to force US armed forces to attack RF interests at home and abroad? POTUS is the commander-in-chief, but, at the same time, he is not allowed to unilaterally decide who may or may not cross the border into the United States. These decisions are, clearly, subject to review by federal judges, as was demonstrated with both of his "travel bans" (which would be more appropriately called "travel restrictions").

Do the judges also have a power to compel armed forces to take actions which a sitting President is refusing to take? Are there any other implications of Congress declaring war which a POTUS does not choose to execute?

I know none of this happened before, but we are in unprecedented territory here, so I am curious to know what kind of warning signs should I watch for when a member of Congress declares that RF has attacked us directly and makes this declaration in her official capacity (not politicking it, but while sitting in her committee chair on Capitol Hill in an open hearing).

EDIT:

Point 1:

As an example of why stating that RF committed acts of war against the United States is significant, here's how the declaration of war against the Empire of Japan was phrased:

"Whereas the Imperial Government of Japan has committed unprovoked acts of war against the Government and the people of the United states of America:

"Therefore be it

"Resolved, etc., That the state of war between the United states and the Imperial Government of Japan which has thus been thrust upon the United States is hereby formally declared; and the President is hereby authorized and directed to employ the entire naval and military forces of the United States and the resources of the Government to carry on war against the Imperial Government of Japan; and to bring the conflict to a successful termination, all of the resources of the country are hereby pledged by the Congress of the United states."

While no such resolution was introduced (so far on 3/23/2017), the justification for war declaration has been cited. It has been cited almost word-for-word as it was previously cited, in at least one, previous resolution making a declaration of war.

Point 2:

This is NOT a question about immigration. I have no interest in any opinions or competing legal theories on whether crossing borders, which are protected and enforced, is considered "unauthorized immigration" or a limited-in-form "invasion". I am going with the opinion that it is universally considered to be a form of invasion if a border is enforced and actively protected. If you wish to challenge such an opinion, please, do so in response to other questions, questions you raise yourself, or in any other forum. I am interested solely in legal views as to what is the answer to my question based on the assumption that all the premises of my question are correct. If you wish to challenge the premises of my question, you will not be answering it to my satisfaction.

EDIT 2:

Since people are clearly not able to separate the issue of border defense from some cases of "immigration", let's open it up to the scope in which so many seem to want to view it.

As a hypothetical, what happens if Congress declares war, POTUS refuses to fight it, but private parties begin to engage agents and armies of the adversary state in private hostile actions? Would POTUS have limited authority to stop them? Would his authority to stop them be more limited than it would be had the war not been declared? Would his attempts to thwart private parties, attempting to execute war actions against a nation with whom we would then be at war, be against policy and would be subject to the same type of criminal prosecution as when no state of war exists?

The reason I think this example pertinent is because judicial constraint on war powers is tantamount to judges' ability to order inaction when the executive deems an action necessary. But any ability to order inaction can be easily turned into an ability to allow an action through administrative rebranding of paramilitary groups as "private" or even "law-enforcement" rather than military. So the actual legal theory which brands certain federal defensive forces as "civilian" may serve the purpose of putting those forces within their own silo of decision-making, making any Presidential attempts to constrain them subject to judicial review. And, in a time of POTUS flatly refusing to prosecute a war declared by Congress, a judiciary would be able to provide (through constraint of executive powers) the power to prosecute such war to the "civilian" defensive forces.

This isn't purely hypothetical, either. This is essentially how it came to be that Lincoln put some of the Supreme Court justices under house arrest. They were interfering with the prosecution of the Civil War.

Any law is only as good as its enforcement mechanism. What enforcement mechanisms exist to prevent judges from enabling separate decision-making silos within the "civilian" defensive forces of the federal government which do not answer to the President because of judicial restraint and which can legally prosecute a war based on Congress' expressed declaration of war?

Answer 1

If President Trump refuses to execute the war, does that become an act of treason on his part?

Probably not, but it depends on the definition of treason. Congress could decide that it is, impeach him, and remove him from office. They could also remove him from office without using the term treason.

Is he required to act on such a resolution?

Not really. As chief executive, he has discretion to prioritize the tasks assigned to him by congress. Furthermore, there is plenty of precedent in international affairs for countries being legally in a state of war without any actual combat or other hostilities.

If he doesn't, is there any recourse other than impeachment to force US armed forces to attack RF interests at home and abroad?

There's always political pressure. But there's no way to relieve the president of his command of the armed forces without relieving him of his office. Aside from impeachment by the congress, this can be temporarily achieved by the cabinet, as specified in the 25th amendment.

POTUS is the commander-in-chief, but, at the same time, he is not allowed to unilaterally decide who may or may not cross the border into the United States.

The president's ability to make immigration policy and the fact that such policy is subject to judicial review are unrelated to his powers as commander in chief. Immigration is a civil and criminal matter, not a military one. The president's powers in this regard are delegated to him by congress, not specified in the constitution. On the other hand, the president's role as commander in chief of the military is explicit in the constitution.

Do the judges also have a power to compel armed forces to take actions which a sitting President is refusing to take?

The judiciary does not have the power to order military operations.

Answer 2

If Congress declared war and President refused to execute, could be treason because President would be giving aid and comfort to a declared enemy, by definition - by not executing his duty.