A conciliatory Senate Majority Leader Harry Reid issued a call for compromise during the lame-duck session that starts next week, while signaling personal opposition to any GOP attempts to put off a decision on the nation’s fiscal challenges.

“I’m not for kicking the can down the road. I think we’ve done that far too much,” the Nevada Democrat said. “We know what the issue is; we need to solve it.”

“I think we should just roll up our sleeves and get it done,” Reid said of an agreement to avert the tax rate increases and automatic spending cuts looming at year’s end.

While Reid says the issue should be addressed during the lame-duck session set to begin next week, Speaker John Boehner (Ohio) and other Republicans have signaled that a “grand bargain” may not be possible until after the new Congress convenes next year. Reid said he spoke with Boehner this morning and did not expect that either one of them would draw firm “lines in the sand” at this point.

“The American people want solutions — and tonight, they’ve responded by renewing our majority,” Boehner said Tuesday night. “With this vote, the American people have also made clear that there is no mandate for raising tax rates.”

On that, Boehner and Reid seem to be in disagreement, although the distinction between tax rates and tax revenues may provide both sides with some wiggle room moving forward.

“There was a message sent to us by the American people,” Reid said. “People making all this money have to contribute a little bit more. And, all the exit polling, all of the polling we’ve done — the vast majority of people support that, including rich people.”

Reid said Democrats do not want to play games with an increase in the debt ceiling that will be required early next year to prevent a federal default.

“If they want to go through that again, fine,” Reid said of Republicans on the debt ceiling stalemate last year.

Reid also said he spoke to President Barack Obama on election night and was encouraged by Obama’s message about working through the looming challenges.

Aside from the “fiscal cliff,” Reid discussed a couple of agenda items for the next Congress, including another attempt at an immigration overhaul. Exit poll data showed Obama winning roughly 70 percent of the Latino vote nationally, according to NBC News, but Reid said Republicans should be on board with immigration legislation not just because of the trouble the GOP has had appealing to that growing voting bloc.

Reid referenced Arizona GOP Sen. John McCain’s past work on an immigration bill with the late Sen. Edward Kennedy (D-Mass.). Reid said the immigration overhaul would be near the top of his agenda for the 113th Congress, but it needs GOP support. “We’re going to have some votes on it,” he said.

He also said the Senate’s operating procedures will need to change in the new Congress to blunt GOP legislative blockades. But he firmly ruled out eliminating filibusters altogether.

“I think that the rules have been abused and that we’re going to work to change them. We’re not going to do away with the filibuster, but we’re going to make the Senate a more meaningful place,” Reid said. Sources have indicated that Reid may push a rules change that requires Senators with objections to hold the floor if they seek to block an agenda item, a change from the current practice where Senators can anonymously place holds on legislation and nominees.

Asked about potential environmental legislation in the wake of superstorm Sandy, Reid referenced recent severe storms and his experience running the Environment and Public Works Committee.

“Climate change is an extremely important issue for me, and I hope we can address it reasonably at some point,” Reid said.

The Nevada Democrat also addressed one parochial issue — his relationship with home-state colleague Dean Heller (R). Heller won a full Senate term on Tuesday, beating out Democratic Rep. Shelley Berkley. Reid’s political apparatus was relentless in attacking Heller, but Reid nonetheless said he expected to be able to work with his colleague over the long term.

“Dean Heller and I have been friends for 25 years,” Reid said, noting that Heller served as secretary of state in Nevada when Reid had his tight election battle against Republican John Ensign in 1998. Ensign later won the Senate seat now held by Heller and entered into a nonaggression pact with Reid, working on a variety of home-state issues until his resignation under an ethics cloud last year.

Reid dismissed talk about a riff with Heller over an Internet gambling measure before the elections.

“As far as big blow-ups, that’s so minor in my life,” Reid said.