President Barack Obama’s pitch for $1.6 trillion in new tax revenue from the wealthy has Republican leaders demanding major entitlement cuts even as they face the potential for a revolt among conservatives.

A defiant group of conservative GOP lawmakers said Wednesday that it would oppose raising revenue in a deal to avert the fiscal cliff unless it came from economic growth.

So any deal will likely come from the unknown quantity of Republicans in both chambers who have expressed a willingness to negotiate — and they’re demanding steep cuts to Medicare and other entitlements.

Obama reiterated his demand for higher tax revenue on the wealthy at his first post-election press conference Wednesday, claiming a mandate to help the middle class while also saying he was prepared to make the tough decisions on trimming entitlement programs.

“I want a big deal. I want a comprehensive deal,” he said ahead of talks Friday with congressional leaders on resolving the fiscal cliff.

But he expressed skepticism about GOP proposals to find new revenue without raising tax rates on people making more than $250,000.

“It’s very difficult to see how you make up that trillion dollars … just by closing loopholes and deductions,” Obama said.

He also rejected the idea of using dynamic scoring — assuming faster growth from lower rates — and said he didn’t want to be caught down the line in a situation where the wealthy escape paying higher taxes and the middle class loses out.

Still, Obama said he would be willing to listen to what Republicans offer Friday.

“I’m not going to just slam the door in their face,” he said, adding that he was “very eager” to do tax reform to make the code more efficient.

Obama’s remarks didn’t immediately signal detente with the GOP.

Ways and Means Chairman Dave Camp dismissed the president’s demand to let the tax cuts for the wealthy expire.

“We don’t have time to waste on offers that are going nowhere,” the Michigan Republican said, suggesting broad tax reform as the solution.

Republicans also repeatedly demanded the president put forward a specific plan to deal with the entitlements in the long term — something he has not done so far.

“Additional revenue should be tied to the only thing that will save the country in the long run, and that is reforming entitlements,” Senate Minority Leader Mitch McConnell, R-Ky., said.

Tennessee Sen. Lamar Alexander, one of the GOP lawmakers who has been pushing hard for a grand bargain, underscored McConnell’s point: “The president has said how much revenue he wants. Let’s hear him be as specific about how he’s going to change the entitlement programs to keep the country from going bankrupt. … Where’s the Obama plan?”

Depending on how many votes they may represent, conservatives appear to be the largest obstacle so far to the efforts of Obama and Speaker John A. Boehner of Ohio to reach a deal.

“We will fight any member in our conference that decides this is a good time to raise taxes,” Rep. Raúl R. Labrador said.

Still, the Idaho Republican said that if presented with a deficit reduction plan of $10 in spending cuts for every $1 in tax increases, “I would probably consider that deal.” Obama backs a proposal involving $2.50 in spending cuts for every dollar of new revenue.

That’s a big gap, yet it actually marks some movement from the conservative wing, which outright rejected even that equation during last year’s debt ceiling confrontation and pressed Republican presidential candidates during the primaries to reject that sort of trade.

Boehner has made keeping the rates from going up his bottom line, believing he can sell other revenue increases that would have been unthinkable in the GOP before the elections but now appear likely given Obama’s veto threat.

As Obama noted repeatedly Wednesday, taxes will go up on everyone unless Republicans agree to extend tax cuts for the middle class now.

Boehner also made moves to expand his reach to the entire caucus during the upcoming negotiations by naming Camp, Budget Chairman Paul D. Ryan of Wisconsin and Energy and Commerce Chairman Fred Upton of Michigan to daily management meetings with the rest of the House GOP leadership, a Boehner spokesman said Wednesday.

As negotiations over the fiscal cliff begin in earnest on Friday at the White House, Boehner is likely to find that keeping the House GOP Conference united will only become more difficult, as many conservatives remain unbowed by the Democrats’ victory at the polls.

“I don’t think we lost by being too conservative and articulating our principles too clearly. I think it was actually the opposite,” said Rep. Tim Huelskamp of Kansas.

Democrats were cheered by Obama’s approach and his push for $1.6 trillion in revenue — double the level he discussed in 2011 as part of a failed deal with Boehner.

“The president has gotten off to a great start,” Sen. Charles E. Schumer said. The New York Democrat cited polls showing 60 percent of voters back eliminating the tax breaks for people making more than $250,000 a year, “so we are sticking to it,” he said.

Obama said his position on extending the Bush tax cuts for the wealthy is not new and was repeatedly argued on the campaign trail. “This shouldn’t surprise anybody,” he said. And he cited polls showing that an even greater majority back his position on the tax cuts than voted for him.

Though Democrats said they were largely pleased with president’s starting position, there could be trouble on the horizon. By Wednesday night, a group of at least 13 Senate Democrats were planning to send a letter to Obama asking him to push for a 1-to-1 ratio of revenue to spending cuts, among other things.

Paul M. Krawzak and Humberto Sanchez contributed to this report.