"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 ChaffetzOvernight Finance: Trump pitches massive tax cuts | Freedom Caucus endorses plan | Dems slam framework | House GOP to move B border wall bill | Officials under fire for private jet use GOP lawmaker pushes to end sports leagues' tax-exempt status Republicans predict Senate ObamaCare repeal would pass House MORE (R-Utah) runs for Hatch's seat. Hatch was joined Wednesday by another Tea Party favorite, Sen. Rand PaulRandal (Rand) Howard PaulHouse bill set to reignite debate on warrantless surveillance Authorizing military force is necessary, but insufficient GOP feuds with outside group over analysis of tax framework 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 HarkinThe Hill's 12:30 Report Distance education: Tumultuous today and yesterday Grassley challenger no stranger to defying odds 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 LeeMichael (Mike) Shumway LeeWhatever you think the Alabama special election means, you’re probably wrong How the effort to replace ObamaCare failed Overnight Regulation: Trump temporarily lifts Jones Act for Puerto Rico | Bill would exempt some banks from Dodd-Frank | Senators unveil driverless car bill MORE (R-Utah) and John HoevenJohn Henry HoevenThe Hill's Whip List: Republicans try again on ObamaCare repeal Air Force One is Trump’s new boardroom Overnight Finance: Trump strikes debt, spending deal with Dems | Deal shocks GOP | Fed’s No. 2 to resign | Trump keeps tax squeeze on red state Dems | House aims to pass budget next week MORE (R-N.D.) also spoke today in favor of amending the Constitution.