Still, the idea that the health care legislation was unconstitutional was dismissed as a fringe argument just six months ago — but last week, a federal judge agreed with that argument. Now, legal scholars are handicapping which Supreme Court justices will do the same.

The repeal amendment reflects a larger, growing debate about federal power at a time when the public’s approval of Congress is at a historic low. In the last several years, many states have passed so-called sovereignty resolutions, largely symbolic, aimed at nullifying federal laws they do not agree with, mostly on health care or gun control.

Tea Party groups and candidates have pushed for a repeal of the 17th Amendment, which took the power to elect United States senators out of the hands of state legislatures. And potential presidential candidates like Mitt Romney and Sarah Palin have tried to appeal to anger at Washington by talking about the importance of the 10th Amendment, which reserves for states any powers not explicitly granted to the federal government in the Constitution.

“Washington has grown far too large and has become far too intrusive, reaching into nearly every aspect of our lives,” Mr. Cantor said this month. “Massive expenditures like the stimulus, unconstitutional mandates like the takeover of health care and intrusions into the private sector like the auto bailouts have threatened the very core of the American free market. The repeal amendment would provide a check on the ever-expanding federal government, protect against Congressional overreach and get the government working for the people again, not the other way around.”

Randy E. Barnett, a law professor at Georgetown who helped draft the amendment, argued that it stood a better chance than others that have failed to win ratification. “This is something state legislatures have an interest in pursuing,” he said, “because it helps them fend off federal encroachment and gives them a seat at the table when Congress is proposing what to do.”