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 McConnellTeacher defeats Kentucky state House majority leader in GOP primary Conservatives leery of FBI deal on informant Lobbying world MORE (R-Ky.) congratulated Toomey and said the amendment was "important."

But on Tuesday morning, Senate Majority Leader Harry ReidHarry Mason ReidMcConnell not yet ready to change rules for Trump nominees The Hill's Morning Report — Sponsored by CVS Health — Trump’s love-hate relationship with the Senate Trump to press GOP on changing Senate rules 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.