"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 ChaffetzFormer chairman appears at House Oversight contempt debate Former chairman appears at House Oversight contempt debate Republicans spend more than million at Trump properties MORE (R-Utah) runs for Hatch's seat. Hatch was joined Wednesday by another Tea Party favorite, Sen. Rand PaulRandal (Rand) Howard PaulOvernight Defense: Pompeo blames Iran for oil tanker attacks | House panel approves 3B defense bill | Trump shares designs for red, white and blue Air Force One Senate rejects effort to block Trump's Qatar, Bahrain arms sales Senate rejects effort to block Trump's Qatar, Bahrain arms sales 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 HarkinThomas (Tom) Richard HarkinStop asking parents to sacrifice Social Security benefits for paid family leave The FDA crackdown on dietary supplements is inadequate Wisconsin lawmaker refuses to cut hair until sign-language bill passes 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 LeeOvernight Defense: Latest on House defense bill markup | Air Force One, low-yield nukes spark debate | House Dems introduce resolutions blocking Saudi arms sales | Trump to send 1,000 troops to Poland Overnight Defense: Latest on House defense bill markup | Air Force One, low-yield nukes spark debate | House Dems introduce resolutions blocking Saudi arms sales | Trump to send 1,000 troops to Poland Senators clinch votes to rebuke Trump on Saudi arms sale MORE (R-Utah) and John HoevenJohn Henry HoevenMcConnell ups pressure on White House to get a budget deal McConnell ups pressure on White House to get a budget deal Senators introduce bill to prevent border agency from selling personal data MORE (R-N.D.) also spoke today in favor of amending the Constitution.