In fact, passage of the Boehner plan in the House is far from assured. Minority Democrats oppose the Republican proposal, and some members of the Tea Party faction of the Republican caucus have pledged to vote against any increase in the debt ceiling on ideological grounds.

Early Tuesday, House Majority Leader Eric Cantor reportedly urged fellow-Republicans to set aside intra-party disagreements and rally behind the Boehner plan.

Senator Reid argued his proposal satisfies key Republican demands: substantial spending cuts and no tax increases.

"If Republicans continue to oppose a reasonable proposal I brought to the floor last night, and which we will vote on in the Senate soon, it will be crystal-clear that Republicans do not care if we default on the debt. That is sad but true," added Reid.

Meanwhile, Senator McConnell blasted President Obama's handling of months of negotiations that have yet to yield an agreement.

"The president can claim to be concerned about this impending crisis. But one question continues to linger above every press conference he has called and every speech he has delivered: where is his plan to resolve it? Republicans have proposed multiple plans," McConnell said.

President Obama has put forth the parameters of a deal as he would like to see it, but left it to bipartisan negotiations to try to hammer out a detailed agreement.

The Obama administration says August 2 is the deadline for raising the debt ceiling. Beyond that date, U.S. Treasury officials say the federal government will have to rely on tax revenue alone to fund its operations. Those revenues are insufficient to cover domestic and foreign expenditures, while also servicing America's $14.3 trillion national debt.