"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 ChaffetzTrump's first dinner out in DC: His own hotel DC residents back Utah rep's primary challenger If Democrats want to take back the White House start now MORE (R-Utah) runs for Hatch's seat. Hatch was joined Wednesday by another Tea Party favorite, Sen. Rand PaulRand PaulConquering Trump returns to conservative summit Rand Paul rejects label of 'Trump's most loyal stooge' GOP healthcare plans push health savings account expansion 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 HarkinGrassley challenger no stranger to defying odds Clinton ally stands between Sanders and chairmanship dream Do candidates care about our health or just how much it costs? 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 LeeLessons from the godfather of regulatory budgeting Congress must reform civil asset forfeiture laws A guide to the committees: Senate MORE (R-Utah) and John HoevenJohn HoevenA guide to the committees: Senate GOP senators unveil bill to give Congress control of consumer bureau budget Dem senator: DeVos bigger threat to education than grizzlies MORE (R-N.D.) also spoke today in favor of amending the Constitution.