As congressional leaders negotiate a deal to raise the nation's debt ceiling, Chris Cillizza explains why any deal they strike will probably come down to the wire. (The Washington Post)

Senate leaders said late Monday that they were closing in on a deal to raise the federal debt limit and end the two-week-old government shutdown, just days before the Treasury Department exhausts its ability to borrow.

The emerging agreement would extend the Treasury Department’s borrowing authority until Feb. 7, reopen the government and fund federal agencies through mid-January, according to aides and lawmakers familiar with the negotiations.

In the meantime, policymakers would launch a new round of talks over broader budget issues in hopes of developing a plan to replace deep automatic spending cuts known as the sequester before Jan. 15. That is when the next round of sequester cuts is scheduled to slice another $20 billion out of agency budgets, primarily from the Pentagon.

The framework under consideration includes only minor changes to President Obama’s signature health-care law, falling well short of defunding it or delaying major provisions as conservative Republicans initially sought. Instead, Republicans would get only new safeguards to ensure that people who receive federal subsidies to purchase health insurance under the law are eligible to receive them.

But talks were hung up over another provision, aides and lawmakers said: a demand by Democrats to delay the law’s “belly button tax,” a levy on existing policies that is set to add $63 per covered person — including spouses and dependents — to the cost of health insurance next year. Republicans derided the proposal as a special favor to organized labor.

Meanwhile, Democrats were resisting a GOP demand to deny Treasury Secretary Jack Lew the use of special measures to extend his borrowing power past Feb. 7. That would give Congress a firm deadline for the next debt-limit increase, with no wiggle room for Treasury Department accountants.

Despite those points of contention, Senate Majority Leader Harry M. Reid (D-Nev.) and Minority Leader Mitch McConnell (R-Ky.) appeared confident that they had developed a framework that could win the approval of Congress and spare the country from a first-ever default on the national debt.

“We’ve had a good day,” McConnell said in a speech closing the Senate for the evening. “I think it’s safe to say we’ve made substantial progress and we look forward to making more progress in the future.”

Reid agreed. “We’ve made tremendous progress. We are not there yet, but tremendous progress. And everyone just needs to be patient,” he said. “Perhaps tomorrow will be a bright day.”

The big question mark Monday evening was whether the emerging agreement could win the approval of the Republican-controlled House, where a small bloc of conservatives has managed to direct GOP strategy.

While McConnell and Reid were at work on a bipartisan compromise, House Budget Committee Chairman Paul Ryan (R-Wis.) was continuing to promote a more partisan bill that would lift the debt limit for only six weeks.

House Speaker John A. Boehner (R-Ohio) met midafternoon with McConnell and then huddled with his own leadership team. Afterward, Majority Whip Kevin McCarthy (R-Calif.) declined to say what path the House would take.

“There’s a lot of different options we still have,” McCarthy said, adding that passing the Ryan plan is “always a possibility.”

There were signs that some House conservatives were growing anxious about the Senate talks. Rep. Raúl R. Labrador (R-Idaho), one of the most hard-line conservatives in the House, accused his Senate colleagues of “pussyfooting around” in the budget battle.

“The problem with Senate Republicans is that they always want to have a fight the next time,” Labrador said on CNN.

But Rep. Tom Cole (R-Okla.), a close Boehner ally, said he was confident that McConnell would not sign off on a deal unless Boehner was convinced that it could win a broad majority of Republicans.

“McConnell, I don’t think, will deliberately put us in a bad position,” Cole said, adding that any agreement that creates a process to litigate broader budget issues would achieve an important GOP goal. “If you’re able to do that and you’re able to get some savings out of the entitlement portion of the budget, those aren’t Republican defeats. They are Republican victories.”

After weeks in which no one was negotiating about anything, Monday was a day of near-constant activity. It began with a two-hour gathering of a bipartisan group of 12 senators led by Sen. Susan Collins (R-Maine), the primary sponsor of a separate proposal that appeared to gain strength Friday before fizzling amid Democratic opposition over the weekend.

After that meeting, the Republican members briefed McConnell and the Democrats briefed Reid. Collins said the group was “continuing to discuss the parameters of a deal” but acknowledged that “there really is a focus on leadership right now.”

Later, Reid ventured twice from his office just off the Senate floor, around the corner and down the hall to McConnell’s office, where the two spoke face to face. At midday, McConnell and Boehner met — the speaker was spied briefly as he made his way down a back hallway from his office to McConnell’s suite for a 25-minute update.

The White House had announced in the morning that Reid, McConnell, Boehner and House Minority Leader Nancy Pelosi (D-Calif.) would come downtown at 3 p.m. to brief the president on their progress. But that meeting was postponed amid concern that it would interrupt the talks just as they were making headway.

With lawmakers trickling slowly back into Washington after a weekend at home, Republican leaders in both chambers decided to delay briefing rank-and-file lawmakers about the day’s developments until everyone was in town Tuesday morning.

It was unclear how things would proceed from there.

Sen. Ted Cruz (R-Tex.), the ringleader of the failed effort to attack the health-care law, waved off questions from reporters about whether he would try to block the Senate from approving an agreement, if one were reached.

“We need to see what the details are,” he said repeatedly.

But Sen. Rand Paul (R-Ky.), another conservative, said he has little appetite for obstruction, even if he does not like the final deal. “We need to get an agreement and open the government back up,” he said.

Still, Sen. Bob Corker (R-Tenn.), who has been close to the talks, acknowledged that the emerging agreement would be “a tough vote.” The misguided assault on the health-care law had diverted attention from more meaningful efforts to overhaul the tax code and rein in spending on Medicare and Social Security, he said. And now time has run out for achieving those goals.

“Let’s just spell out what’s happened: We’ve basically blown the last two months with some of our members and a lot of the House focused on a shiny object that was never going to happen,” he said. “To try to put something together in three days that has meaningful things we all would like to see in it is just not possible.”

As talks intensified, Obama warned that if the standoff is not resolved by Thursday, when the Treasury Department will run out of borrowing authority, “we stand a good chance of defaulting.”

U.S. financial markets fell slightly in morning trading but then stabilized. The Standard & Poor’s 500-stock index and the Dow Jones industrial average each dropped about 0.5 percent in the first 90 minutes of trading before rebounding to close with gains. In a more telling sign of market sentiment, the Vix, a measure of expected future volatility in stock markets, soared more than 12 percent before ending the trading day up 2.2 percent.

Bond markets were closed for the Columbus Day holiday. In recent days, investors have sold off short-term Treasury bills maturing later in October, fearful that there could be disruptions that prevent the government from making good on its obligations.

Jackie Kucinich contributed to this report.