"All 47 Republican members of the Senate are of one mind of the need for a balanced-budget amendment to the Constitution," Hatch added.

Hatch is expected to be in a tough Senate race in 2012, particularly if Tea Party favorite Rep. Jason ChaffetzJason ChaffetzChaffetz: Threats against lawmakers should be taken seriously Gowdy won't use Oversight gavel to probe Russia The Hill's 12:30 Report MORE (R-Utah) runs for Hatch's seat. Hatch was joined Wednesday by another Tea Party favorite, Sen. Rand PaulRand PaulGOP at decisive moment on Planned Parenthood Trump: ‘I cannot imagine’ GOP senators don’t back healthcare bill Sunday shows preview: Senate healthcare debate heats up MORE (R-Ky.), who argued that at least three-quarters of U.S. citizens say Congress would do a better job if a balanced-budget amendment were in place.

"I really don't understand how a vast majority of the public can be for this and yet this body still refuses to act," Paul said in a colloquy with Hatch. Hatch replied that Congress has historically made "excuses" for not living within its means.

Paul added that an amendment "may well be what forces us to really have the discussion" about how to rein in spending.

Hatch also dismissed ideas like legislative spending caps. "I've got to tell you that has never worked," he said. "We've got to put straitjacket onto this matter where the Congress has to live like 49 states have to live."

Only Vermont does not have a requirement to balance the state budget.

Under the amendment as described by Hatch, federal spending would be limited to 18 percent of U.S. gross domestic product (GDP). Amending the Constitution requires a two-thirds majority in both the House and Senate, and then ratification by three-fourths of the states.

Sen. Tom HarkinTom HarkinDistance education: Tumultuous today and yesterday Grassley challenger no stranger to defying odds Clinton ally stands between Sanders and chairmanship dream MORE (D-Iowa) spoke immediately after Republicans on the floor, and indicated the strength of Democratic opposition to a balanced-budget amendment. Harkin said the last time federal spending was 18 percent of GDP was in 1967, before the Medicare program was fully under way.

"What the Republicans are saying is that if they can get that down to 18 percent, we can do away with Medicare, which is what they want to do anyway," Harkin said. "Republicans want to do away with Medicare."

Sens. Mike LeeMike LeeGOP at decisive moment on Planned Parenthood Trump: ‘I cannot imagine’ GOP senators don’t back healthcare bill Trump called Cruz to press him on ObamaCare repeal bill: report MORE (R-Utah) and John HoevenJohn HoevenGOP considers keeping ObamaCare taxes Senators want governors involved in health talks Republicans go to battle over pre-existing conditions MORE (R-N.D.) also spoke today in favor of amending the Constitution.