The same mechanisms that exist to ensure they don't enact legislation excess of any of its constitutional powers. Someone raises a challenge by defying their law, and the court (usually an appeals court, I would imagine) makes a ruling whether or not the law in question is indeed constitutional. Yes, that means judges have to get involved at some point. That's not what I have a problem with. I can even forgive them if their legal reasoning is different from mine. But certain things I consider unacceptable are: deciding a case based on whether or not they think it would be good for society; "compelling government interest"; saying that the Constitution is a "living" document, and therefore has to "adapt" to our changing "needs"; making rulings based on whether or not the results thereof would fit in with what was supposedly envisioned by the draftsmen (such as racial voting statistics); failing to delineate their legal reasoning, instead resorting to airy-fairy "principles"; to name a few.
Okay, so first, we have the power of the judiciary to hold that a statute is unconstitutional. In that regard, do you agree with the Supreme Court's claim in Marbury v. Madison (1803) that the Court has that power?
Second, we have the power of the President to veto the legislation and, at a minimum, delay the Congress by requiring that it pass the legislation with a super-majority.
Third, we have the power of the people to elect to the Congress and the presidency persons who will respect the views of the people regarding the appropriate boundaries of Congressional power.
Assuming that you accept the propriety of judicial review, how should the Supreme Court actually review a statute like the one we were discussing which suspended the use of literacy tests? Congress was authorized to suspend the literacy tests because they were being used by certain states to deny or abridge the right of black citizens to vote. Did the Court actually make that factual finding itself - that the literacy tests were in fact being used to discriminate against blacks? Or did the Court just accept that fact as accurate because Congress declared that Congress had found that fact to be true? Should the Court just accept the accuracy of Congressional findings? As a practical matter, does it have any choice? How could the Court independently determine the accuracy of Congressional findings?
These turn out to be the pivotal questions in terms of whether or not the Supreme Court can impose meaningful internal limitations on the legislation of Congress. If the Court cannot find sensible means by which it can review the accuracy of Congressional findings, the Court's role, as a practical matter, becomes limited to declaring an act of Congress unconstitutional only when the act violates a specific prohibition in the Constitution (e.g. the Bill of Rights).