Updated: 3:59 p.m.

Senate Majority Leader Harry Reid said Sunday that he is “cautiously optimistic” that a deal can be reached to avert a government default before the Treasury’s Tuesday deadline, even as his own proposal was blocked in an afternoon vote.

While opening the floor for a rare Sunday session, the Nevada Democrat emphasized that leaders only had a few hours left to resolve the outstanding questions plaguing the latest potential agreement to emerge.

That plan would raise the debt ceiling by about $2.4 trillion, which would cover the country through the 2012 elections and would set up a two-step method for achieving about $3 trillion in deficit reduction, including a proposed enforcement mechanism that would kick in the second round of savings later this year that is sure to be highly unpopular with Democratic rank and file. Congressional Republicans and the White House had negotiated across-the-board spending cuts, including significant dents into entitlement programs, if a special committee established by the new legislation fails to produce a workable deal to provide $1.8 trillion in savings in the second round.

“After speaking with [Minority] Leader Mitch McConnell [R-Ky.] this morning we’re, we’re cautiously optimistic,” Reid said. “There are a number of issues yet to be resolved, and we must understand that no agreement has been made. We’re optimistic that one can be reached, but we’re not there yet.”

“[But] optimism in days past has been stomped on,” Reid said, referring to multiple breakdowns in talks over the past few weeks, including when Republicans backed out of a negotiating group led by Vice President Joseph Biden and Speaker John Boehner (R-Ohio) pulled out of talks with President Barack Obama — twice.

Republicans blocked, 50-49, a different plan to raise the debt ceiling on Sunday afternoon, 12 hours after the vote was originally scheduled to take place. Reid had unveiled the proposal during an impasse in negotiations early last week, and he voted against his own measure Sunday so that he could call it back to the floor if Democrats and Republicans reach an agreement in the latest round of talks. The maneuver keeps the underlying bill available as the vehicle to send legislation back to the House so lawmakers can dispatch it to the president’s desk — they hope before Tuesday’s deadline.

Three Members who caucus with Democrats — Sens. Bernie Sanders (I-Vt.), Ben Nelson (D-Neb.) and Joe Manchin (D-W.Va.) — voted against the Reid plan. One Republican, Sen. Scott Brown (Mass.), voted in favor.

Earlier in the day, Reid emphasized that the vote would not seriously effect the potential to get a bill to Obama on time.

“No matter the outcome of this vote … the message will still be before this body. If there is an agreement that can be met, this is the vehicle to be used to send it back to the House,” Reid said.

The pending $3 trillion agreement between the White House and Congressional leaders is set to include $1.2 trillion in discretionary spending cuts up front, with the remainder to be found by a bipartisan joint Congressional committee by Thanksgiving. The enforcement mechanism — what Senate Democratic Conference Vice Chairman Charles Schumer (D-N.Y.) described earlier Sunday as the “swords hanging over” lawmakers’ heads to make sure the committee reaches agreement — is the remaining point of contention.

“Obviously, the sword over the head of Democrats is the cuts. What is the sword over the Republicans? It has to be equal,” Schumer said on CNN’s “State of the Union.”

Including more cuts to defense spending — an approach the GOP has opposed throughout the course of budget negotiations — as part of the enforcement mechanism could be a way to “equalize” the agreement.