Top level negotiations will continue until Sunday afternoon at one p.m. after Senate Majority leader Harry Reid delayed a test vote on a Democratic debt ceiling increase plan.
Reid told reporters late Saturday that there was "still a distance to go" before a deal could be reached, according to Reuters.
Negotiations, which have included the White House, began again on Saturday, after the House and Senate rejected each others' proposals.
Earlier on Saturday, McConnell said a deal was attainable in the "near future, although Democrat leader Sen. Harry Reid said at the time negotiations are still far apart.
An initial test vote on the Democratic plan at one a.m. on Sunday had been scheduled, although Republicans had indicated they would have blocked the proposal.