"[The] election's over and we have enormous challenges ahead of us right here, and we have to sit down and go to work on it now, not wait," he said during a news conference.
Voters re-elected President Obama, kept the Senate in Democratic hands and kept the House of Representatives under control of Republicans.
"[The] American people want us to work together. Republicans want us to work together. Democrats want us to work together," Reid said. "They want a balanced approach to everything, but especially the situation we have dealing with this huge deficit, and taxes are a part of that."
Taking a swipe at Senate Minority Leader Mitch McConnell's comments made four years ago, Reid said, "This was really the message the American people sent from all over, and that is they're tired of the partisan gridlock, they're tired of things like, 'Well, I have one goal: defeat Obama.'"
Noting the time for excuses is over, Reid said, "It's time we get to work. We can achieve really big things when we work together. ... I'm going to do everything within my power to be as conciliatory as possible. I want to work together, but I -- I want everyone to also understand you can't push us around. We want to work together."
Compromise, he said, "is not a dirty word," adding that he was willing to negotiate any time.
"And so I am convinced that we need to start working together a lot. Gridlock is not the solution," Reid said. "It's the problem."
Reid said he talked with House Speaker John Boehner, R-Ohio, about working to avert the looming automatic cuts in spending and the expiration of lower tax rates enacted during President George W. Bush's administration.
Reid said he and his staff have "a fine relationship" with the speaker and his staff.
"This isn't something that I'm going to draw any lines in the sand, he's not going to draw any lines in the sand, I don't believe, and I think we need to work together," Reid said.
Reid also said he would consider changing, not eliminating, the filibuster rules "to make the Senate a more meaningful place."
Republicans used the filibuster to block legislation because Democrats lacked the 60 votes needed to end debate.
"I think that the rules have been abused and that we're going to work to change them," he said.