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Republican lawmakers scrambled back to the drawing board to modify their plan for a short-term increase in the debt ceiling, after President Obama apparently pushed back on the proposal during a high-stakes White House meeting.

Discussions between the two sides continued into the night Thursday after the meeting broke up with no deal announced, despite optimism earlier in the day that the two sides might agree. Senate Democratic Leader Harry Reid also cast doubt on House Speaker John Boehner's plan.

Despite both sides claiming to be working together, the day ended like it began, with Americans still unsure when the partial government shutdown will end, and the financial markets still uncertain as to whether the country might miss next week's deadline to raise the debt ceiling.

Obama is expected to meet White House meeting Friday with GOP senators, who may offer alternative options for funding the government and ending the standoff over the debt limit.

Sen. Susan Collins, R-Maine, and others have endorsed a proposal that would fund the government for six months and repeal ObamaCare's medical device tax and give federal agencies greater flexibility to manage across-the-board spending cuts caused by sequestration.

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    The sticking point appears to be whether to end the partial government shutdown as part of any deal to lift the debt ceiling.

    The original House GOP plan called for a six-week extension of the debt ceiling with no strings attached -- but would not resolve the partial government shutdown. Instead, Republicans wanted Obama and Democrats to make a "real commitment" to negotiate over the partial government shutdown and a longer-term debt-ceiling hike as the next step.

    Fox News is told that Obama pushed back on that plan. Rep. Hal Rogers, R-Ky., said Obama wants to make sure the partial government shutdown is also lifted as part of any debt-ceiling agreement.

    The White House said in a brief statement that "no specific determination was made" but Obama "looks forward to making continued progress with members on both sides of the aisle."

    House GOP Leader Eric Cantor said the meeting was useful, and that there would be more conversations into the night. Republican plans to begin working on their stopgap bill late Thursday also were put on hold, indicating a change in strategy.

    What the pause says about the prospects for a deal is unclear. Boehner would still have a hard time bridging the demands of the rank-and-file, who want conditions put on any budget bill, and the demands of Obama, who wants a "clean" bill.

    But Obama and Senate Majority Leader Harry Reid both appeared to push back on GOP attempts to push a bill that does not deal with the partial shutdown.

    "Not going to happen," Reid said of the possibility of any negotiations while the partial shutdown is still in effect.

    Reid addressed the plan after his own meeting at the White House. The White House simultaneously issued a statement that appeared to back Reid up, saying "the president and the Senate Democrats will continue to pursue reasonable discussions about our budget challenges after these manufactured crises end."

    The White House, though, gave muddy and conflicting statements throughout the day.

    Earlier, White House Press Secretary Jay Carney said Obama could support Boehner's plan as is. He said that if a "clean" bill to hike the debt ceiling for six weeks hits Obama's desk, "He would sign that."

    Carney said Obama would strongly prefer that Congress approve a longer-term increase in the debt ceiling and approve a spending bill right away. But pressed repeatedly by reporters, Carney appeared to open the door to a short-term increase in the debt limit even if the partial government shutdown is not addressed.

    The subsequent statements by Reid and the White House appeared to walk that back. However, Reid also said the Senate would look at and consider anything the House sends over -- leaving open the possibility that a short-term debt ceiling hike could be considered if it's the only option.

    Time is running out to resolve the debt-ceiling impasse. By Oct. 17, Treasury officials say the nation will be unable to pay all its bills.

    The goal of the GOP proposal appeared to be to buy time, by removing the immediate threat of missing the Oct. 17 deadline, for both sides to strike a broader agreement on spending and debt.

    "It's time for leadership," Boehner said Thursday morning.

    Inside the GOP caucus, reaction to the Republican leaders' plan appeared to be mixed, with some voicing support and others voicing skepticism. Some Republican senators were privately saying any bill to raise the debt ceiling should also end the partial government shutdown.

    Sources said the initial GOP proposal would increase the debt ceiling through a hard deadline of Nov. 22, but also call for negotiators to be appointed to discuss the budget -- and require Obama to work with them on both the debt limit and budget.

    Pressure is increasing on all sides to work out an agreement. Treasury Secretary Jacob Lew testified on Thursday that both stalemates are creating a drag on the economy and Wall Street.

    He issued dire warnings about failing to raise the debt ceiling. He did not specifically warn that the government would be unable to pay interest on the debt, but said payments ranging from Social Security checks to Medicare reimbursements to military salaries could be halted by the end of the month.

    He said some of the repercussions would be unpredictable since this is "uncharted territory."

    "It would be chaos," Lew said.

    Though some Republicans have accused the administration of exaggerating, many still do not want to toy with breaching the debt-ceiling deadline.

    Fox News' Mike Emanuel, Ed Henry, Chad Pergram and Fox Business Network's Rich Edson contributed to this report.