McConnell (R-Ky.) said he was “hopeful and optimistic” about the outcome.
Their comments came after an hour-long negotiating session with Obama on how to avoid the so-called fiscal cliff. Obama plans to speak at 5:45 p.m. Eastern time.
The president and the congressional leaders are trying to avert the economy-slowing combination of tax increases and spending cuts set to hit in the new year.
Reid, McConnell, House Speaker John A. Boehner (R-Ohio) and House Democratic Leader Nancy Pelosi (D-San Francisco) emerged from the meeting separately, each avoiding the cameras and ignoring questions shouted by reporters.
Pelosi later told reporters in the Capitol that Reid and McConnell had agreed to try to come up with proposal. She described the meeting as "constructive" and "candid."
Boehner repeated his position that the House would wait for the Senate to act.
The meeting of the foursome and the president was the first since mid-November, when the group declared they were willing to find common ground to avoid the deadline.
Since then, talks between Obama and Boehner, who leads the Republican House, have broken down and lawmakers have put the effort on hold during the holiday break. The meeting Friday was the first major attempt to restart negotiations before the Dec. 31 deadline.
Obama went into the meeting laying out the proposal he pitched before Christmas. The president wants to allow income taxes to rise on income over $250,000 and extend unemployment benefits.
A source familiar with the meeting said the president planned to ask Republican leaders for a counter-proposal -- or an up-or-down vote on his.