A state-level campaign to rein in the federal government by calling an unprecedented convention to amend the U.S. Constitution is gaining steam, picking up support from two high-profile Republicans as more states explore the idea.

The latest figures to endorse the effort are retired Oklahoma Sen. Tom Coburn and Ohio Gov. John Kasich.

Coburn, a legendary government-waste watchdog, announced this week that he has joined the effort by becoming a senior adviser for the group Convention of States Action, which wants states, not just Congress, to pass constitutional amendments. A primary goal is to get an amendment to the Constitution requiring a balanced federal budget, in which spending does not exceed revenue.

Article V of the Constitution says amendments can be ratified either by Congress or by states if two-thirds of them petition Congress to call a convention. Then, any amendment proposed at the convention must be ratified by three-fourth, or 38, states.

So far, the Alaska, Florida and Georgia legislatures have each passed a resolution in support of a convention, and 25 more are considering one, according to the group.

“Our founders anticipated the federal government might get out of control,” Coburn said Tuesday. “And they gave us a constitutional mechanism to rein it in.”

Beyond getting Congress to pass a balanced budget, supporters of the largely Republican-backed effort are also focused on such issues as campaign finance reform and making sure the Environmental Protection Agency doesn’t over regulate.

Kasich, a potential 2016 White House candidate, has recently concluded a six-state tour in which he asked legislators to support the convention, largely to push the balanced budget idea.

“Who the heck thinks we should keep spending without any regard to the consequences?” Kasich, a fiscal hawk and former House Budget Committee chairman, asked in South Dakota. “I don’t care if you’re a Republican, a Democrat or a Martian. This is not what we should be doing as a nation. It’s irresponsible.”

Kasich, who claims credit for crafting a balanced federal budget before leaving Congress in 2000, gave a similar pitch last month in Utah, urging state lawmakers to pass a convention resolution, which has failed there in past years.

However, he faced some surprising crosswind in the largely conservative state, skepticism about the idea from GOP Sen. Mike Lee.

The Tea Party-backed Lee has sponsored a balanced-budget amendment every year since getting elected to the Senate in 2010. But he reportedly is concerned about a convention creating the potential for a barrage of bad amendments.

Wisconsin GOP state Rep. Chris Kapenga has helped drive the effort through the group the Assembly of State Legislatures, which is focused on crafting a clear set of convention rules to allay such concerns and counter arguments like Lee’s.

“Where taking away the fear of the unknown,” he told FoxNews.com earlier this week.

Kapenga also said his state legislature is working on a balanced budget proposal that he’s “fairly certain” will pass and serve as Wisconsin’s notice to Congress.

Still, he acknowledges supporters of the effort won’t get past the 34-state threshold until they convince some Democratic-leaning legislatures to join.

“Red and blue states still have some differences that need to be ironed out,” Kapenga said.

The effort is also being pushed by Citizens for Self-Government, which is trying to get the minimum number of states or more to pass the resolution.

All 27 constitutional amendments have been passed by Congress, and any effort to help states take away that authority appears unlikely.

Still, the effort also has support from Louisiana Gov. Bobby Jindal, 2008 vice presidential candidate and former Alaska Gov. Sarah Palin and former Arkansas Gov. and potential 2016 White House candidate Mike Huckabee -- all Republicans.

The Associated Press contributed to this report.