"I'd like to see us follow and understand the Constitution," he said. "That's going to lead to some places I might like and some places I might not like. But what I like best is that we're a nation of laws and not men, and we should follow our laws."
Others have begun advocating the reining in of federal government through other means. Barnett and a group of tea party activists are working on a proposal for a constitutional amendment that would effectively give state legislatures veto power over federal laws.
Another often-cited approach is the repeal of the 16th and 17th amendments. The 16th Amendment overturned an 1896 Supreme Court ruling invalidating a federal income tax. Repealing it would be a swift blow to federal programs.
Others have called for the repeal of the 17th Amendment, which established the popular election of senators. It's a proposal that strikes some as odd, particularly coming from a movement often branded populist.
"Turning [Senate elections] back over to state legislatures, it is an anti-democratic movement, which is really unusual in politics," said Stanford's Kramer.
But advocates for the repeal say the nation's founders gave the state legislatures the power to elect senators as a check on federal power.
In practice, legislatures were often deadlocked in Senate elections, which often brought state business to a standstill, said Ralph Rossum, a constitutional law professor at Claremont McKenna College and author of "Federalism, the Supreme Court, and the 17th Amendment: The Irony of Constitutional Democracy."
"The founders put this great power in their laps, and all it was was a curse," Rossum said.
The problem with cleaving to the Founding Fathers' approach, Kramer said, was that so many of their best-laid plans went awry.
"Really, nearly all their major assumptions were wrong," he said. "The separation of powers didn't work the way they thought it would. The assumptions about federalism didn't pan out," he said, forcing pragmatic adaptations.
Some see that pragmatism at play in the calls for a reconsideration of the 14th Amendment, passed after the Civil War to ensure citizenship for former slaves.
A change could mean children of illegal immigrants would not automatically be given citizenship. Graham has said in a series of interviews that the founders could not have anticipated that women might come to the U.S. just to give birth.
Others argued that the Supreme Court has long misread language in the amendment granting citizenship to those born in the U.S. "and subject to the jurisdiction thereof." Jurisdiction, they suggest, could refer to national allegiance, although this is not the common definition of the word.
Homeland Security Secretary Janet Napolitano said last week that messing with the amendment is "just wrong."