Also Saturday, President Barack Obama met at the White House with Reid and Sens. Dick Durbin of Illinois, Chuck Schumer of New York and Patty Murray of Washington, to discuss their options after the House rejected Democrats' efforts to hold a vote on ending the budget impasse and Senate Republicans filibustered Reid's proposal for a bill to extend the federal government's borrowing authority until after the 2014 elections.
The White House did not immediately issue a statement on the substance of the meeting.
Reid and McConnell were discussing the potential for a bipartisan compromise based on a proposal by Sen. Susan Collins, R-Maine, to fund the government for six months and raise the debt ceiling until Jan. 31, The Hill reported.
"The fact that they're actually talking for the first time represents significant progress," said Senate Republican Whip John Cornyn, R-Texas.
"The real conversation that matters now is the one that's taking place between McConnell and Reid," said Sen. Bob Corker, R-Tenn. "We're at place where something important has evolved."
Senate Democrats Saturday rejected Collins offer earlier in the day, with Appropriations Committee Chairwoman Barbara Mikulski of Maryland arguing a six-month funding bill is insufficient.
Collins' proposal included a two-year delay in a tax on medical devices whose purpose is to help cover the cost of the Affordable Care Act.
The Senate voted 53-45 in favor of moving Reid's bill to a floor debate, but 60 votes were required. The bill would raise the federal borrowing limit by more than $1 trillion, The Hill reported.
The White House issued a statement saying it was "unfortunate that the common sense, clean debt limit increase proposed by Senate Democrats was refused a yes or no vote today."
"This bill would have taken the threat of default off the table, and given our nation's businesses and the economy the certainty we need," the statement said. "With five days until the government runs out of borrowing authority, Congress needs to move forward with a solution that reopens the government and allows us to pay our bills so we can move on to the business of achieving a broader budget deal that creates jobs, grows the economy and strengthens the middle class."
House Speaker John Boehner, R-Ohio, held a closed-door meeting with GOP members Saturday and reported afterward the situation remained deadlocked despite the looming expiration of the government's borrowing authority, which the Treasury Department has said will arrive Oct. 17.
Boehner had no official statement after Saturday's meeting, but Rep. Richard Hudson, R-N.C., told reporters Boehner told his troops there was "no deal" and "no negotiations."
Rep. Paul Labrador, R-Idaho, said the House was looking to Republicans in the Senate to push through a spending deal because the talks with the House had stalled.
"It's up to the Senate Republicans ... the president rejected our deal," he said.
President Barack Obama told business leaders during a conference call Friday he was hopeful a deal would be reached this weekend, USA Today said.
The House proposal calls for negotiations with Obama on entitlement and tax reform in exchange for a short-term increase in the debt ceiling. Obama has not agreed to the proposal, which The Hill said leaves Boehner in a political jam between determined conservative Republicans and the public backlash against the GOP.
Boehner appeared to be getting some additional pressure from Republican allies to get a deal done that would reopen the government and raise the debt ceiling, The Washington Post said Saturday.
Leaders of the business community met with White House officials on Friday for a closed-door briefing on the standoff.
"I do think we need to act. We need to combine and concentrate our efforts to succeed," said Bruce Josten, executive vice president of the U.S. Chamber of Commerce. "But the equation is complicated and requires very good information."
Republicans on Capitol Hill played down the notion the Republicans had no coherent strategy in its dealings with the administration.
"There are plates spinning everywhere. Everybody's now trying to work on this," Rep. James Lankford, R-Okla., told The Hill. "It is just confusing to try to figure out what's the deal that's actually getting traction."