The historical record on the question is probably too thin to yield a well-supported answer as to the due diligence and the underlying "what were they thinking" question, that is, I doubt there is any record of any original debate where one side demands resolution of the contradiction, and how that charge was answered.
The American Law of Taxation: As Determined in the Courts of Last Resort gives a summary of the ensuing case law relationship between taxation and compensation, as of 1884 (p. 31 of the book, p. 100 in the PDF):
Taxation differs from the power of eminent domain in this: that it has
no thought of compensation by way of return for that which it takes
and applies to the public good, further than all derive benefit from
the purposes to which it is applied; in other words, that the support
of government and other objects of public utility promoted by taxation
are supposed to return to the individual the same which has been taken
from him, as his share of the public burden
The limitation in the constitution that private property shall not be
taken for public use, refers solely to the right of eminent domain,
and not to taxation or special assessments for local benefits.
(both quotes with long lists of supporting state law citations). The New York case People v. Mayor of Brooklyn, 4 N.Y. 419 apparently overturned its prior ruling (I think the citation is 6 Barb. 214, which I can't track down), commenting on the earlier ruling on an assessment.
The supreme court reversed and annulled the assessment, holding...
That money is property; that it can not be taken from a
citizen for public use by the right of eminent domain, without just
compensation; and that the enhancement in value of the relators'
lands, by the grading and paving of Flushing avenue, is not that just
compensation within the meaning of the constitution.
The later court gets out of this, noting that
Taxation exacts money, or services, from individuals, as and for their
respective shares of contribution to any public burden. Private
property taken for public use by right of eminent domain, is taken not
as the owner's share of contribution to a public burden, but as so
much beyond his share. Special compensation is therefore to be made in
the latter case, because the government is a debtor for the property
so taken; but not in the former, because the payment of taxes is a
duty and creates no obligation to repay, otherwise than in the proper
application of the tax.
Taxation operates upon a community or upon a class of persons in a
community and by some rule of apportionment. The exercise of the right
of eminent domain operates upon an individual, and without reference
to the amount, or value exacted from any other individual, or class of
In other words, the Takings and Just Compensation clauses are understood to be about the power of eminent domain, which specially burdens the individual, and that is distinct from the general burdening of society that is taxation.
There are, as far as I know, no finely-tuned SCOTUS rulings on the relation between the Just Compensation clause and the tax and spend clause. There is case law that holds that there is no contradiction between the power to tax and the Fifth Amendment. For example McCray v. US, 195 U.S. 27:
While both the Fifth and Tenth Amendments qualify, insofar as they are
applicable, all the provisions of the Constitution, nothing in either
of them operates to take away the grant of power to tax conferred by
the Constitution upon Congress, and that power being unrestrained
except as limited by the Constitution, Congress may select the objects
upon which the tax shall be levied, and, in exerting the power, no
want of due process of law can possibly result, and the judiciary
cannot usurp the functions of the legislature in order to control that
branch of the Government in exercising its lawful functions.
And Brushaber v. Union Pacific, 240 U.S. 1:
So far as the due process clause of the Fifth Amendment is relied
upon, it suffices to say that there is no basis for such reliance,
since it is equally well settled that such clause is not a limitation
upon the taxing power conferred upon Congress by the Constitution; in
other words, that the Constitution does not conflict with itself by
conferring, upon the one hand, a taxing power, and taking the same
power away, on the other, by the limitations of the due process
This however says that taxation laws do not violate the due process requirement.