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Senate Democratic Leader Harry Reid has signed off on a tentative debt-ceiling compromise, saying he hopes lawmakers can finalize a deal and move to a vote as early as Sunday.

At the same time, concerns were spreading on the conservative side that the emerging plan could cut too deeply into defense spending, raising questions about whether the framework can attract enough bipartisan support.

One congressional source said the deal is not yet sealed. But Reid, becoming the first congressional leader to publicly endorse the plan, said late Sunday afternoon through a spokesman that he had signed off on it "pending caucus approval."

But as time dragged on and House Speaker John Boehner, scheduled a conference telephone call with his rank and file, the likelihood of any vote Sunday night appeared less likely.

With pressure intensifying to produce a bill that can somehow sail through both chambers in the next two days, leaders on both sides are now scrambling to not only finalize the package but loop in their rank-and-file members.

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Already, liberal groups and lawmakers were raising alarm about the possibility of entitlement cuts in the package. House Democratic Leader Nancy Pelosi, without taking a position, said she'd have to review the details, looking ahead to a meeting with Democrats on Monday.

"We all may not be able to support it. And maybe none of us will be able to support it," she said.

But as Reid tried to build support on the Democratic side, GOP leaders were dealing with mounting concerns from party conservatives about possible defense cuts.

Under the framework, the plan would immediately cut spending by about $900 billion over the next decade, and then task a commission to recommend another set of cuts that would, taken together, add up to the size of the debt-ceiling increase. If the committee's recommendations are not approved by the end of the year, a "trigger" in the proposal would automatically enact across-the-board cuts -- with roughly half of the cuts coming from defense, sources said.

One Republican source warned that a "large bloc" of GOP lawmakers would oppose the deal if those cuts are too deep, noting that there are dozens of Republicans on the House Armed Services Committee alone who "agree with the unanimous chorus from senior military leadership -- we're at the bare minimum for (defense) spending without deeply damaging an already stressed force."

Connecticut Sen. Joe Lieberman, a hawkish independent, also is "very concerned about rumors that the debt agreement now being negotiated will disproportionately cut defense spending and result in unacceptably high risk to our national security," according to a spokesman.

But a GOP leadership source predicted that such concerns will be allayed when the agreement is unveiled.

With lawmakers facing an Aug. 2 deadline to either raise the debt cap or face the possibility of default, Congress is running out of time for do-overs.

The Senate, after voting against House Republicans' proposal Friday night, effectively killed Reid's counterproposal Sunday afternoon. Sixty votes were required to advance the proposal, and it fell far short in a 50-49 roll call. While the test vote was expected to fail, the outcome stressed how important it is for the latest round of talks to produce a viable alternative.

Reid said he was "cautiously optimistic." Senate Republican Leader Mitch McConnell said lawmakers are "really, really close to an agreement."

Sens. Dick Durbin, D-Ill., and Jon Kyl, R-Ariz., the No. 2 senators in their respective parties, also said on "Fox News Sunday" that they were feeling better about the discussions.

"I have a much more positive feeling than I did 24 hours ago," Durbin said.

Though White House senior adviser David Plouffe cautioned there's no deal yet, Senate leaders are in dire need of a compromise.

Reid won over just one Republican supporter, Massachusetts Sen. Scott Brown, for his bill Sunday afternoon. On the Democratic side, he lost Nebraska Sen. Ben Nelson, West Virginia Sen. Joe Manchin, and Vermont Sen. Bernie Sanders, an independent aligned with Democrats.

Lawmakers have until Aug. 2 to raise the $14.3 trillion debt ceiling. The Obama administration says that after Tuesday, the Treasury can no longer pay all of America's bills.

"There's no question we're approaching the final hour," Gene Sperling, director of the National Economic Council, told "Fox News Sunday."

Sources said the tentative arrangement between the White House and Republicans closely resembles the plan first proffered by House Speaker John Boehner before he modified it to appease Tea Party conservatives.

Sources said the debt ceiling would be raised by as much as $2.4 trillion, with a roughly equal amount of deficit-reduction. Though sources said the debt-ceiling increase would be split into two parts, Congress would have to meet a very high threshold to stop it -- likely assuring President Obama an increase that lasts until early 2013, as he requested.

But the framework of the deal floated perilously between the alternatives pushed by House conservatives and Senate Democrats.

The tentative plan would have Congress vote on a balanced-budget amendment -- a key demand of Tea Party-aligned Republicans -- but would not require Congress to approve it in order for the debt ceiling to be raised.

Top aides to House GOP lawmakers told Fox News they were concerned about the emerging deal. One source said it could be difficult to bring House conservatives back on board with such a plan.

At the same time, the tentative arrangement is closer to Boehner's original bill than Reid's.

The partisan makeup of Congress makes the task of striking a deal that much more complicated.

Neither party controls a supermajority in the Senate, making it necessary to attract bipartisan support in order to pass a bill.

Republicans hold a broad majority in the House, but conservatives may be skeptical of any deal that has too many Democratic fingerprints on it from the Senate side.

House Republican Whip Kevin McCarthy, R-Calif., told "Fox News Sunday," that the talks were moving in the "right direction" but that House Republicans would "have to look at the details."

Fox News' Mike Emanuel, Trish Turner and Ed Henry contributed to this report.