Republicans are attempting to gain leverage in the debt-ceiling debate to force the president to accept another measure Toomey endorsed during his speech — a constitutional amendment that would force the government to balance its budget.

"We are rapidly approaching that limit and we will get there sometime soon," said Toomey. "I would like to see a balanced-budget amendment, and one with real teeth."

In January, Rep. Tom McClintock (R-Calif.) introduced a companion bill in the House. The government is projected to hit its debt ceiling as early as April, and it is possible House GOP leadership will call up McClintock's amendment for consideration then.

Both Senate leaders have weighed in on the amendment to the patent reform bill.

Immediately following Toomey's speech, Senate Minority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellSenate passes 0B defense bill Overnight Health Care: New GOP ObamaCare repeal bill gains momentum Overnight Finance: CBO to release limited analysis of ObamaCare repeal bill | DOJ investigates Equifax stock sales | House weighs tougher rules for banks dealing with North Korea MORE (R-Ky.) congratulated Toomey and said the amendment was "important."

But on Tuesday morning, Senate Majority Leader Harry ReidHarry ReidThe Memo: Trump pulls off a stone-cold stunner The Memo: Ending DACA a risky move for Trump Manchin pressed from both sides in reelection fight MORE (D-Nev.) complained that the amendment was not germane to the underlying legislation, and predicted it would not get far.

"One of the first amendments filed had nothing to do with patent reform and we will dispose of that,” said Reid.

—This story was updated at 5:03 p.m.