WASHINGTON » The Senate’s top two leaders both expressed optimism today that they were closing in on an agreement to prevent a national financial default and reopen the government after a two-week partial shutdown.

After meeting twice today with his Republican counterpart, Democratic Majority Leader Harry Reid opened the Senate session by saying he was ‘very optimistic we will reach an agreement this week that’s reasonable in nature." Moments later, Republican leader Mitch McConnell seconded Reid’s view.

They spoke after what McConnell termed "a couple of very useful discussions."

Officials in both parties said House and Senate negotiators would be appointed to seek a deficit-reduction agreement that could ease or eliminate a new round of automatic spending cuts scheduled to take effect in January. While the current round of these cuts fell on both domestic programs and defense, the upcoming reductions would hit primarily the Pentagon.

The officials said the two leaders were discussing legislation to raise the $16.7 trillion debt limit until spring. It was not clear if that would permit Treasury Secretary Jacob Lew to employ a series of steps that could add additional months to the extension, as administrations in both parties have done in recent years.

In addition to raising the debt limit and reopening the government, officials said, the two leaders were discussing a possible tightening in income verification requirements for individuals who qualify for subsidies under the health care law known as Obamacare. Democrats were resisting a Republican-backed proposal to suspend a medical device tax that was enacted as part of the health care law. The tax is widely unpopular among lawmakers in both parties, but the outcome of that disagreement remained unclear.

These officials spoke on condition of anonymity, saying they were not authorized to discuss private matters.

While Reid, D-Nev., said there was not yet an accord, he said he hoped to have a proposal to outline when the two men and House leaders meet with Obama at mid-afternoon. Emerging from Reid’s office, Sen. Amy Klobuchar, D-Minn., said "he told us the negotiations were productive and positive."

No details were available on the terms under discussion.

Visiting a Washington charity, Obama mentioned the possible progress in the Senate and said his mid-afternoon meeting will determine whether it’s real.

"My hope is that a spirit of cooperation will move us forward over the next few hours," the president told reporters.

Otherwise, he warned that the threat of default was legitimate.

"If we don’t start making some real progress both in the House and the Senate, and if Republicans aren’t willing to set aside some of their partisan concerns in order to do what’s right for the country, we stand a good chance of defaulting," he said.

In announcing the meeting with Obama, the White House said the president would repeat a vow he has made consistently in recent weeks: "we will not pay a ransom for Congress reopening the government and raising the debt limit."

The two Senate leaders, Reid and McConnell, had spoken by phone Sunday but failed to agree on a deal to raise the nation’s borrowing authority above the $16.7 trillion debt limit or reopen the government. Congress is racing the clock with Treasury Secretary Jack Lew warning that the U.S. will quickly exhaust its ability to pay the bills on Thursday.

Separately, a bipartisan group led by Sen. Susan Collins, R-Maine, met for two hours this morning on a possible solution to the impasse.

"We’re making very good progress, but there’s still many details to be worked out," Collins said before joining her GOP colleagues at a meeting with McConnell. "We don’t have a finished, agreed-upon product yet but I think we had an excellent meeting. And we’ll get together later today."

There was no certainty that the growing anxiety among financial leaders around the world would provide the necessary jolt to Senate leaders, who represent the last, best chance for a resolution after talks between President Barack Obama and House Republican leaders collapsed.

Sen. Joe Manchin, D-W.Va., said today that investors are growing increasingly "skittish" about the possibility of default. The bond markets were closed for Columbus Day, and by mid-morning the stock market was down modestly, with both the Dow Jones industrial average and Standard & Poor’s 500 index losing less than 1 percent. Trading in Asia was muted, with markets in Tokyo and Hong Kong closed for holidays.

The shutdown has furloughed 350,000 federal workers, impeded various government services, put continued operations of the federal courts in doubt and stopped the IRS from processing tax refunds. Some parks and monuments remain closed, drawing a protest at the National World War II Memorial on Sunday that included tea party-backed lawmakers who had unsuccessfully demanded defunding of Obama’s 3-year-old health care law in exchange for keeping the government open.

Economists see greater financial danger from an historical default. Christine Lagarde, the International Monetary Fund’s managing director, spoke fearfully about the disruption and uncertainty, warning on Sunday of a "risk of tipping, yet again, into recession" after the fitful recovery from 2008.

Reid and McConnell — five-term senators hardened by budget disputes and years of negotiations — are at an impasse over the automatic, across-the-board spending cuts known as sequestration and whether to undo or change them as part of a budget deal. Republicans want to keep the spending at the deficit-cutting level of the 2011 budget law while Democrats are pressing for a higher amount.

"I’m optimistic about the prospects for a positive conclusion to the issues before this country today," Reid said as the Senate wrapped up a rare Sunday session.

McConnell insisted a solution was readily available as he embraced the proposal from a bipartisan group of 12 senators, led by Collins and Manchin, that would re-open the government and fund it at current levels for six months while raising the debt limit through Jan. 31.

It also would give agencies greater flexibility in dealing with the automatic budget cuts, delay the medical device tax for two years and establish income verification for individuals receiving subsidies to buy health insurance.

"It’s time for Democrat leaders to take ‘yes’ for an answer," McConnell said in a statement.

"This haven’t put us on suicide watch yet," Manchin joked this morning, "but they’re concerned about us."

He said, "The leaders have to come together" and decide what time frame a stopgap spending bill would cover and how much it would cost.

Tennessee’s Sen. Bob Corker, a Republican, said the leaders of both parties need to be "getting on the same page."

McConnell and Republicans want to continue current spending at $986.7 billion and leave untouched the new round of cuts on Jan. 15 that would reduce the amount to $967 billion. Democrats want to figure out a way to undo the reductions, plus a long-term extension of the debt limit increase and a short-term spending bill to reopen the government.

"Republicans want to do it with entitlement cuts," said Sen. Chuck Schumer, D-N.Y. "Democrats want to do it with a mix of mandatory cuts, some entitlements and revenues. And so how do you overcome that dilemma? We’re not going to overcome it in the next day or two."

He suggested keeping the government running through mid-January.