President Obama traveled to this Philadelphia suburb Friday to deliver the same sharp message he gave directly to House Speaker John A. Boehner earlier in the week: Get on board with the White House’s tax proposal, or get out of the way.

The relationship between the two most powerful men in Washington, who together will effectively decide the fate of negotiations over the feared “fiscal cliff,” has broken down badly since the heady days 17 months ago when they shared a golf course.

Obama’s 14-minute speech at a toy manufacturing company here amounted to a verbal poke in the eye, warning that taxes will go up without a plan — and likening Boehner and other Republicans to one of the most reviled figures of the holiday season.

“That’s sort of like the lump of coal you get for Christmas,” Obama said at K’nex, the maker of Tinkertoys. “That’s a Scrooge Christmas.”

Boehner (R-Ohio) fired back less than an hour later on Capitol Hill, saying House Republicans had reached a “stalemate” with the White House. “It’s not a serious proposal,” he said of Obama’s plan.

The increasingly antagonistic tone has stoked fears in Washington and on Wall Street that an inability to compromise, or even communicate, could lead the country over the fiscal cliff, a series of automatic tax increases and spending cuts that are to take effect in January. Economists have warned that the measures could jolt the economy back toward recession.

Any political negotiation involves a good deal of bluster, particularly in Washington. Such discussions often involve a period of theatrical posturing, even as staffers continue to hammer out specifics behind closed doors. Both sides also have reason to play to their respective constituencies, even if some level of compromise is inevitable.

White House advisers point to the president’s conversations with Boehner — including a 28-minute phone call Wednesday — as evidence that they are still on speaking terms and that Obama is not trying to bypass Congress.

But Obama’s trip to Pennsylvania signaled that the administration is fully committed to a much tougher and more aggressive approach in dealing with congressional Republicans on the eve of a second term. The president’s advisers believe he has no choice but to play hardball with the GOP after the gridlock of the past two years, and they are confident that Obama holds the upper hand with the public, given his solid election victory and the strong support found in polls for higher taxes on the richest Americans.

Obama, who generally avoids schmoozing even his closest allies, invited Rep. Allyson Y. Schwartz (D-Pa.) to accompany him on Air Force One. He visited a decidedly purple political county, where several Republican House members might be susceptible to public pressure to get behind Obama’s proposals. And he was touring a company whose chief executive said he supports Obama’s tax plan even though it would raise federal rates on the factory.

Obama playfully suggested that he would be keeping score once he was back at the White House.

“I’ve been keeping my own naughty and nice lists for Washington,” Obama told the crowd at the toy factory. “So you should keep your eye on who gets K’nex this year. There are going to be some members of Congress who get them, and some who don’t.”

The message was heard loud and clear on Capitol Hill, where House Republicans have opposed Obama’s demand that the George W. Bush-era tax cuts expire for net household income over $250,000 a year to help pay down the $16.3 trillion national debt.

GOP leaders have said they are willing to accept some new revenues, perhaps in the form of a cap on tax deductions and loopholes, as long as Obama accepts cuts to spending entitlements such as Medicare and Medicaid.

“The impression everyone’s gotten is that he’s sort of still in campaign mode,” Sen. Jon Kyl (R-Ariz.) said of Obama. “He believes he can get 100 percent of what he wants and is therefore not required to negotiate and has presented a sort of take-it-or-leave-it proposition.”

Obama has told associates that he personally likes Boehner, but their relationship has soured since the breakdown of the debt ceiling negotiations in 2011 that led to the nation’s first-ever credit rating downgrade. Obama thought they had reached agreement on a “grand bargain” of spending cuts and revenue increases.

Both sides have said they felt betrayed when the deal fell apart. Obama concluded that he could no longer trust Boehner to deliver votes from the tea party wing of his conference, and the White House switched to a more aggressive approach.

Boehner has been to the White House three times since, according to his office. The most recent was Nov. 16, when Obama met with Boehner, Senate Majority Leader Harry M. Reid (D-Nev.), Senate Minority Leader Mitch McConnell (R-Ky.) and House Minority Leader Nancy Pelosi (D-Calif.).

The five leaders expressed optimism that day, but they did not specify common ground on the key sticking points, including taxes.

Earlier this week, Treasury Secretary Timothy F. Geithner delivered a proposal to lawmakers that included $4.5 billion in reduced borrowing over the next decade. Administration officials said Friday that Obama is also proposing to delay automatic spending cuts through Aug. 1 to give Congress a limited amount of time to hatch a deal.

The overall savings figure includes about $1.2 trillion in savings already in force as part of previous spending agreements with the Republican House, plus $1 trillion in fresh revenue from the expiration in January of the Bush high-end tax cuts. Another $1.2 trillion would come next year, about half from rewriting the tax code and half from spending cuts, including changes to Medicare and Medicaid, officials said.

Boehner and other Republicans characterized the Obama proposal as a nonstarter.

“What you see is what you get,” Boehner said Friday. “And while I may be affable and someone that can work with members of both parties, which I’ve demonstrated over the 22 years that I’ve been here, I’m also rather determined to solve our spending problem and to solve this looming debt crisis that is about to consume us.”

The GOP has long groused that Obama has shied from the kind of informal social interactions or frequent cross-aisle communications that could help grease deals. Republicans say there’s been no thawing since his reelection.

But White House press secretary Jay Carney scoffed at the idea that Obama has sidestepped Boehner during the talks.

“There were a lot of meetings, a lot of conversations,” Carney said. “But the president also, very appropriately, went out into the country to make sure that the American people were engaged in this and that their voices were heard in this kind of debate. And that’s what he’s doing again because that’s how it should be.”

Rosalind S. Helderman, Paul Kane and Lori Montgomery contributed to this report. Nakamura reported from Washington.