WASHINGTON (MarketWatch) — An agreement with President Obama to raise the U.S. debt limit, cut federal spending and avert a default is very close, Senate Republican leader Mitch McConnell said Sunday.

“We’re very close,” the Kentucky Republican said during an appearance on CNN’s State of the Union. “We had a very good day yesterday.”

McConnell didn’t divulge any details beyond saying there would be no taxes increases. Other media reports said the core is a $3 trillion package.

On NBC’s “Meet the Press,” Obama adviser David Plouffe said there had been progress in negotiations that ran into the late-night hours on Saturday, but said there wasn’t yet a deal.

Late Saturday, Democrat Harry Reid of Nevada, the Senate majority leader, called off a cloture vote that could have paved the way for another vote on his own plan to increase the debt limit. Reid revised his proposal after House Republicans rejected it.

Reid said he was making the move to give negotiations more time.

Words of optimism on debt talks

Leaders of both parties huddled, negotiated and argued throughout Saturday on a number of proposals. At one point Republicans hinted that they were close to a compromise with President Obama.

Although Reid shot down the idea of an imminent agreement, negotiations continued late into the night and at least one news report suggested the two sides were close to an agreement.

The president wants Congress to raise the debt ceiling — the legal limit on how much the government can borrow — by $2 trillion-plus to avoid the need for another increase before the 2012 election.

Republicans want a corresponding reduction in federal spending that matches the size of the increase in the debt limit — without raising taxes.

Whatever emerges from negotiations between Republicans and the White House is likely to be a combination of the plans. Democrats would get a debt-limit increase that extends beyond the 2012 election and Republicans would win substantial cuts in spending, with a mechanism put in place to automatically enforce cuts if the two parties could not agree.

Earlier Saturday, McConnell suggested he was negotiating directly with Obama.

“We are now fully engaged with the one person in America ... who can sign a bill into law,” said McConnell. “I’m confident and optimistic that we’re going to get an agreement in the very near future.”

Even as McConnell offered soothing words, Republicans in the Senate dragged out a debate on the merits of Reid’s proposal. Some 43 Republican senators said in a letter to Reid that they opposed his initial plan, forcing him to rewrite it. Read the letter (external link).

Before the Senate votes Sunday, Democrats need to muster an agreement with Republican leaders or somehow find 60 votes to avoid a filibuster.

Earlier Saturday, Obama restated his call for a deal and once again warned of the consequences of a U.S. default — another salvo in the president’s campaign to pile on the pressure to make a deal to raise the $14.3 trillion debt limit.

“We need to reach a compromise by Tuesday so that our country will have the ability to pay its bills on time,” said Obama in his weekly address.

Administration officials, economists and business leaders have warned of economic repercussions at home and around the world if the U.S. defaults.

Senate tables Boehner's debt bill

Late Friday, the House of Representatives on a 218-210 vote, passed a Republican bill assembled by Speaker John Boehner (R., Ohio) that included provisions for a balanced budget.

The bill was swiftly shot down in the Senate, but in a tit-for-tat, the House rejected Reid’s proposal to put the parties back at square one.

Boehner’s plan would lift the limit by $900 billion and cut about the same amount in spending. It would also require Congress to vote on a balanced-budget amendment before the limit would be raised again.

Reid’s plan would shave off more than $2 trillion in government spending in the next 10 years and raise the debt limit by about $2.4 trillion — an amount that would mean no further debt-limit adjustments until after the 2012 election.

The divisions on Capitol Hill have already taken their toll on the U.S. economy. The S&P 500 Index SPX, +0.82% and Dow Jones Industrial Average DJIA, +1.19% both saw their biggest weekly drops in more than year, falling about 4%. Read about the falls in Market Snapshot.

Market turmoil was further highlighted by the fact that Treasury yields on Friday saw their biggest fall of the year. Read about falling Treasury yields.

And the flight to safety is also seeing heavy withdrawals from money-market funds and into bank deposit accounts, according to Saturday’s Wall Street Journal. Read about the flight to cash.

The Tuesday deadline imposed by the administration and expected uncertainty before it’s reached will also affect the stock market in the coming week. Read about the week ahead.