President Obama cracked open the door to compromise with Republicans on tax rates for the nation’s wealthiest households Wednesday, saying he is “open to new ideas” for increasing their tax bills without letting the top rate rise as scheduled in January to 39.6 percent.

Obama flatly rejected Republican calls to let the top rate remain at 35 percent, where it has stood for more than a decade under legislation adopted during the George W. Bush administration. And he shot down a GOP proposal to cap deductions for mortgage interest, charitable giving and other expenses in return for extending the Bush-era tax rates for the wealthy.

But in a break with the position he took on the campaign trail, Obama said he would not insist on drawing “red lines” around 39.6 percent, the rate in effect for top earners during the Clinton administration. Democrats familiar with White House thinking said Obama is willing to set the top rate somewhat lower — around 37 percent or 38 percent — as long as the overall burden grows for families earning more than $250,000 a year.

“With respect to the tax rates, I just want to emphasize I am open to new ideas,” Obama said at a White House news conference. “If the Republican counterparts, or some Democrats, have a great idea for us to raise revenue, maintain progressivity, make sure the middle class isn’t getting hit, reduces our deficit, encourages growth, I’m not going to just slam the door in their face. I want to hear ideas from everybody.”

It was not clear how Obama’s concession would affect negotiations over the “fiscal cliff,” a massive accumulation of expiring tax breaks and spending cuts that threatens to throw the nation back into recession early next year. With talks scheduled to start Friday at the White House, House Speaker John A. Boehner (R-Ohio) and other GOP leaders have offered to raise fresh tax revenue, but only if Democrats agree to restrain spending on health and retirement programs and to rewrite the tax code to push the top rate even lower than 35 percent.

At a news conference immediately after his reelection Wednesday as speaker, Boehner said he remains “optimistic.”

“If you look closely at what the president had to say and you look closely at what I had to say, there are no barriers here to sitting down and beginning to work through this process,” he said. “I don’t think anyone on either side of the aisle underestimates the difficulty that faces us.”

Other top Republicans reacted with annoyance to the president’s remarks. House Ways and Means Committee Chairman Dave Camp (Mich.) said Wednesday’s news conference marked the third time since the election that Obama has publicly discussed the fiscal cliff without offering an explicit path forward. And with Obama set to leave Friday for Southeast Asia, Camp said, negotiations are unlikely to begin in earnest until after the Thanksgiving break.

“Time is running short, and, frankly, we don’t have time to waste on offers that are going nowhere,” Camp said in a statement.

Democrats countered that Obama has laid out a very specific plan in recent days. That plan seeks not only to end the Bush tax cuts for the wealthy but also to raise even more money from top earners — a total of $1.6 trillion over the next decade, double the sum Boehner offered in 2011 debt-reduction talks with Obama.

On Wednesday, Obama suggested raising the money in two stages — first, by letting the Bush rates lapse on income over $250,000 a year while extending them for 98 percent of U.S. households. The expiring Bush tax cuts constitute the biggest piece of the fiscal cliff, and extending the cuts for the middle class would mean “half of the danger to our economy is removed by that single step,” Obama said.

Then, Obama suggested that policymakers adopt a “framework” to achieve additional savings next year by overhauling tax laws and restructuring federal health programs. Obama pronounced himself “eager” to simplify the tax code and to work with Republicans on a far-reaching plan to restrain the government borrowing that has become a stain on his presidency. “I want a big deal,” he said. “I want a comprehensive deal.”

Obama’s most recent budget request sought to raise taxes on the wealthy and corporations by a similar $1.5 trillion. The administration estimates that returning to Clinton-era rates for top earners would generate about $850 billion over the next decade. Tack on an increase in the estate tax and the figure rises to about $1 trillion.

Some Republicans have suggested replacing that tax revenue by capping deductions, an idea promoted by GOP presidential candidate Mitt Romney. The non-partisan Tax Policy Center estimates that setting the cap at $17,000 — for all taxpayers — would do the job. And Obama’s budget proposes raising nearly $600 billion by limiting the value of deductions for top earners.

Democrats are reluctant, however, to swap higher tax rates for deduction caps, noting that the move could have a painful effect on charities and other parts of the economy. “It’s very difficult to see how you make up that trillion dollars — if we’re serious about deficit reduction — just by closing loopholes and deductions,” Obama said. “You know, the math tends not to work.”

Moreover, eliminating tax breaks for the wealthy now would make it harder to raise revenue later through tax reform without hitting the middle class, Democrats say.

“The president has been absolutely clear that a balanced approach to reducing the deficit requires high-income individuals to provide the revenue necessary for an agreement,” said Rep. Chris Van Hollen (Md.), the ranking Democrat on the House Budget Committee. “You can’t get the necessary revenue without the top rates going to Clinton-era levels.”

Obama has pressed that goal in meetings this week, first with liberal groups and then Wednesday with the chief executives of some of the nation’s largest corporations. Many attendees represented companies that are big players in Republican politics. Chevron, for example, made the largest known corporate contribution to a political entity this year: $2.5 million to the Congressional Leadership Fund, a super PAC established by Boehner allies. And Aetna’s 2010 contributions to the U.S. Chamber of Commerce and the American Action Network, two GOP-oriented nonprofit groups, totaled more than $7 million.

Administration officials hope the executives will give Republicans political cover to accept higher taxes as part of broader debt-reduction deal. After the meeting, Honeywell chief executive David Cote, who served on Obama’s fiscal commission, predicted on Bloomberg television that the fiscal cliff would at last force action.

“I have always felt confident,” he said, “that . . . the president understood the issue overall and that it had to be both tax and entitlement reform if you truly wanted something that protected the country.”

Tom Hamburger contributed to this report.