A deal to raise the federal debt ceiling and avoid the first ever U.S. default is "very close," but House Democratic Leader Nancy Pelosi said Sunday there is a chance they may not pass it.

"We all may not be able to support it, or none us may be able to support it," Pelosi told reporters late Sunday night.

Earlier Senate Majority Leader Harry Reid said Sunday afternoon that he hopes a vote can happen Sunday evening to avoid a default by an Aug. 2 deadline, according to Reuters.

Top level negotiations were continuing on Sunday after an early afternoon attempt by Reid to see if one of his proposals would have enough votes to clear the Senate. It fell short of the 60 "ayes" needed to overcome a Republican Party filibuster. It could only manage a 50-49 vote in favor.

The deal currently being negotiated by McConnell and Vice President Joe Biden included a rise in the federal debt limit in two stages, for a total of $2.2 trillion. The increase would be large enough not to need another raise beyond the 2012 general election.

On Friday, the Senate blocked a bill passed by the House handily, setting the stage for further negotiations.

Republicans and Democrats have been in discussions for months regarding the debt limit as the deadline has approached.

Leaders Remain Optimistic

Reid, a Democrat, remained "cautiously optimistic" a deal could be reached.

With 43 Republicans pledging to vote against his plan, Reid pushed ahead Sunday even though it was clear he wouldn't get the needed 60 votes to clear the hurdle in the Senate.

Fifty Senators on Sunday voted for cloture (to end the debate), including one Republican, Massachusetts Sen. Scott Brown.

And 49 senators voted against cloture, including Democrats Ben Nelson, Joe Manchin and independent Bernie Sanders.

Democrats fell 10 votes short of the needed 60 to overcome a Republican filibuster.

Reid actually voted "no" on his own bill, in the effort to keep the underlying bill alive to bring back later if and when agreement is reached for the anticipated deal between the White House and Congressional leaders.

He felt though that pushing ahead was necessary so the effort remained in attack mode to reach a compromise before the Aug. 2 deadline to raise the U.S. debt ceiling.

"Optimism in days past has been really stomped on at times," Reid said. "As we know, one problem can stop the whole agreement."

The Senate could return to vote on the plan Sunday evening if an agreement is reached.

Meanwhile, Republican Senate Republican leader Mitch McConnell said Sunday negotiators are "very, very close" to a deal to raise the debt ceiling, beating an Aug. 2 deadline.

Some Democrats, however, talking in a more cautious tone. The deal is not yet done, they say.

As McConnell announced in two interviews over the weekend that a deal is close, Sen. Chuck Schumer, D-N.Y., told CNN there is a sense of relief in Washington that progress is being made but that "there is no final agreement" yet on the table.

Schumer later told CBS in an interview Sunday that one of the final sticking points between Republican and Democratic leaders is the creation of a "trigger" mechanism that would strike at priorities of both parties of the bipartisan committee does not come up with a plan for further deficit reduction.

Trigger proposals being discussed include automatically reducing spending on entitlement programs including Medicare along with closing tax loopholes or reducing defense and non-defense programs by an equal amount.

"It should be equally tough on Democrats and Republicans," Schumer said.

But even though final details remain in discussion, McConnell talked Sunday as if a deal would get done before the Aug. 2 deadline to raise the U.S. debt ceiling.

A Congress has been working overtime, around the clock, to meet an approaching Aug. 2 deadline to ward off a first-ever government default, and the Senate prepared Sunday to convene in a rare session to address the issue.

McConnell (R-Ky.) said progress was made late Saturday in discussions between the White House and congressional leaders on a debt-ceiling plan that could find enough support from both Democrats and Republicans to get an agreed upon plan to President Barack Obama by the Aug. 2 deadline.

On CNN's "State of the Union" McConnell told about a $3 trillion plan that includes cuts in federal discretionary spending, a vote on a balanced budget amendment, and caps on future spending.

The plan would also form a joint committee to consider additional budget cuts and entitlement reforms that Congress could vote on in the fall, in addressing America's $14 trillion budget deficit.

If approved, the plan would raise the debt ceiling, now at its limit, until after the 2012 presidential election. But even though progress has been made over the weekend, it's not done yet.

"This deal has not been finalized but I think we're very, very close to something I could comfortably recommend to my members, and I believe the Democratic leadership will be doing the same," said McConnell, on CBS' "Face the Nation."

Sen. Dick Durbin of Illinois, the No. 2 Democrat in the Senate, expressed similar optimism about getting a deal done.

"I have a much more positive feeling than I did 24 hours ago," Durbin told Fox News Sunday.

Lawmakers came under intense public pressure Friday as no deal was in sight and U.S. and global markets dropped in response to America's financial uncertainty. China and other countries, as well as U.S. banks and other companies, have called upon lawmakers to reach agreement so the U.S. doesn't default, possibly sending the nation back into another recession.

David Plouffe, senior advisor to Obama, said Sunday morning that Republican and Democratic leaders in discussions "still have some work to do."

"We're talking about a variety of options here," Plouffe said.

He added that if negotiators do not reach an agreement by Tuesday, the day of the deadline to raise the debt ceiling, the White House would consider raising the debt ceiling for a day or two to work out final plan details.

The Senate is set to vote Sunday afternoon on the developing plan.