Senate Majority Leader Harry M. Reid (D-Nev.) offered a carrot-and-stick approach to congressional Republicans on Wednesday, vowing to “dance” with his counterparts in bipartisan cooperation, but pledging to “fight” them with rules changes if they tried to unilaterally obstruct President Obama’s second term.

Following elections that gave his party unexpected gains in the Senate, Reid said voters had delivered a message that the two parties need to work together, beginning with the so-called fiscal cliff negotiations to avert a set of automatic tax hikes and spending cuts set to kick in — at more than $500 billion next year alone — in January without action.

“They’re tired of this partisan gridlock,” Reid said at a midday press conference.

Reid, however, rejected the approach offered by House Speaker John A. Boehner (R-Ohio), whose caucus will maintain a strong hold on that chamber’s majority. Reid reiterated his demand for a “balanced approach” that would include allowing the George W. Bush-era cuts to expire for the wealthy, which could bring in up to $800 billion in new revenue over the next decade.

On Tuesday night, Boehner said that voters had said “no” to tax hikes as part of the potential deal.

The respective leaders of the two chambers spoke by phone Wednesday morning, Reid said, with Boehner slated to speak to reporters later Wednesday. Despite the public posturing on taxes, Reid said the two had agreed not to “draw lines in the sand.”

That said, Reid reiterated his vow to try to change Senate rules to limit the use of filibuster tactics by the minority, an arcane policy dispute that has the potential to become a major flash point in the weeks ahead. “You can’t push us around,” Reid declared.

While he did not outline his proposal Wednesday, Reid has in the past supported a rules change that would limit the minority to just one vote to filibuster each piece of legislation, as opposed to the current rules that allow for at least two filibuster votes. Even when the majority has more than 60 votes needed to choke off a filibuster, the multiple hoops required to do so can take up to a week of legislative floor time.

Republicans have previously rejected any effort to revamp the filibuster rules, and Reid may resort to altering the rules through a party-line vote at the start of next year, reversing decades of precedent in which such changes are done by a two-thirds majority.

Politically, Reid agreed with many analysts that GOP presidential nominee Mitt Romney and many Senate GOP candidates had lost their races because the party’s policy positions on immigration and social issues had driven Hispanics and women far away from Republicans.

“We’re the party of diversity,” Reid said, noting that one third of his caucus — that will likely hold 55 Democrats — will be women.

Reid pledged to bring immigration legislation to the Senate floor, daring Republicans to block the measures “at their peril.”

In laying out his hopes for a bipartisan agenda, Reid recalled his elevation to Democratic leader eight years ago, when he assumed the post in a similar position Senate Minority Leader Mitch McConnell (R-Ky.) finds himself, with a newly reelected president of the opposing party and just 45 members of his caucus. Reid, a former amateur boxer, said at the time that he would rather “dance” with Bush and Senate Republicans than “fight” with them, a pledge he reiterated Wednesday.

“I don’t dance as well as I fight, but I’d much rather do that,” he said.