The White House has threatened to veto House Speaker John Boehner's plan for raising the federal debt limit.
Boehner is trying to get enough votes for his two-step budget plan, which includes a short-term bill to cut spending by about $1.2 trillion and extend the debt ceiling for about six months.
Senator Harry Reid unveiled his own plan, which counts an extra trillion dollars in savings by winding down the wars in Iraq and Afghanistan.
While both proposals would create a bipartisan congressional commission to identify cuts in social programs, Reid's plan extends the debt ceiling beyond the 2012 elections.
Republican Senator Mitch McConnell said both sides have to compromise to get a plan that will pass the House of Representatives and the Senate.
"We're going to have to get back together and get a solution here. We cannot get a perfect solution, from my point of view, controlling only the House of Representatives, so I'm prepared to accept something less than perfect because perfect is not achievable," McConnell said.
A vote on Boehner's plan is set for Wednesday.
If no deal is place by August 2, the United States could default and not be able to pay its bills.
During his address to the nation Monday night, President Barack Obama said a default itself would be reckless and irresponsible.
He accused Republicans of standing in the way of a balanced compromise by ruling out any tax increases.