A vote is not yet scheduled on Toomey's amendment, according to a leadership aide.
Toomey's legislation would allow the government to avoid defaulting on its debts if the $14.3 trillion limit were reached, by requiring the Treasury Department to pay principal and interest on public debt before making any other payments. A companion bill has been introduced in the House by members of the Republican Study Committee.
The bills serve as pushback to dire warnings delivered by Treasury Secretary Timothy Geithner. In a Jan. 6 letter to all lawmakers, Geithner said that if they let the government hit the ceiling, there could be "catastrophic economic consequences" both in America and across the globe.
"Never in our history has Congress failed to increase the debt limit when necessary," he wrote. "Failure to increase the limit would be deeply irresponsible."
Toomey and other Republicans have accused Geithner of employing scare tactics in the debt-limit debate, and Toomey said the legislation would take the specter of default off the rhetorical table.
"Failing to raise the debt ceiling is not a desirable situation and would be disruptive, but the worst thing we can do is simply continue the irresponsible deficit spending that jeopardizes our economic future," he said when he introduced the bill Jan. 25.
While Republican leaders have acknowledged the debt limit will need to be raised, conservatives are still pushing for serious spending cuts to accompany their support. Some lawmakers are trying to tie a vote on raising the debt limit to one that would add a balanced-budget amendment to the Constitution.
The Treasury most recently said it expects to hit the debt limit sometime between Apr. 5 and May 31.
Toomey's measure has 18 co-sponsors, but with Democrats still retaining a majority in the Senate, the amendment's chances are slim.