House Republican leaders are changing their plans for Boehner’s “Plan B” tax proposal as vote counts show the margin extraordinarily close.

( PHOTOS: Fiscal cliff’s key players)

GOP leadership is considering attaching a package of spending cuts to ride alongside Boehner’s tax rate bill. Republican lawmakers are skittish about voting on allowing taxes to snap to near 40 percent for millionaires without paring back federal spending.

Simultaneously, Republican leadership scrapped a plan to vote on the Senate’s tax rate proposal, which extended Bush-era tax rates for income below $250,000. Republicans are looking to keep their message tight, sources said.

Amid signs that negotiations are stalled, Obama stepped out first, telling reporters at the White House that it is “puzzling” that Republicans haven’t accepted his latest fiscal cliff offer when they’re only separated by a few hundred billion dollars in spending cuts.

“Take the deal,” Obama said.

( Also on POLITICO: Cliff talks turn into public posturing)

Boehner responded a short time later with a 54-second statement from the Capitol, rejecting the president’s offer and announcing his intention to push forward with a vote Thursday on his so-called Plan B bill that raises taxes on income above $1 million.

“The president will have a decision to make,” Boehner said just before he abruptly left the room. “He can call upon Senate Democrats to pass that bill or he can be responsible for the largest tax increase in American history.”

The dueling statements Wednesday were an attempt by both parties to frame the high-stakes debate over the fiscal cliff and pin blame on the other side if Washington fails to deal with more than $500 billion in spending cuts and tax hikes, which are scheduled to go into effect in the new year.

Substantive talks have ground to a halt since Boehner announced he would pursue a Plan B bill that raises tax rates but does nothing to deal with across-the-board spending cuts known as the sequester, reduce entitlement spending or address a host of expiring provisions.

The administration issued a veto threat earlier Wednesday in a signal to Boehner that he should abandon the fallback bill and reengage in the talks on a $2 trillion budget package.

( Also on POLITICO: “Plan B” stalls in Senate)

Obama said he is willing to continue talks with Boehner. But the two have not spoken since Monday night, when the speaker informed him of the alternate strategy. Obama said he would reach out to congressional leadership over the next few days in an attempt to learn why Capitol Hill isn’t making progress.

“I remain, not only open to conversations, but I remain eager to get something done,” Obama said. “I’d like to get it done before Christmas. There’s been a lot of posturing up on Capitol Hill instead of just going ahead and getting stuff done. We’ve been wasting a lot of time. It is the right thing to do. I’m prepared to get it done, but they’re going to have to go ahead and make — make some adjustments.”

Senior administration officials said Wednesday that Boehner’s decision to pursue a fallback strategy has made it even more difficult to reach a deal and raised the chances of going off the fiscal cliff.

( Also on POLITICO: Cliff talks turn into public posturing)

“We have put forward real cuts in spending that are hard to do — in every category,” Obama said. “And by any measure, any traditional calculation, by measures Republicans themselves have used in the past, this would be as large a piece of deficit reduction as we’ve seen in the last 20 years.”

Obama, at turns conciliatory and confrontational, invoked the shooting in Connecticut and Hurricane Sandy to argue that “the country deserves folks to be willing to compromise on behalf of the greater good.”

“If this past week has done anything, it should just give us some perspective,” Obama said. “If you just pull back from the immediate, you know, political battles, if you kind of peel off the partisan war paint, then we should be able to get something done.”

Obama rejected the Republican argument that he hasn’t offered enough spending cuts, saying it’s “not going to fly” because he is proposing nearly $1 trillion in reductions — although the GOP has taken issue with the White House’s calculation.

“Frankly, up until a couple of days ago, if you looked at it, the Republicans in the House and Speaker Boehner, I think, were in a position to say, ‘We’ve gotten a fair deal,’” Obama said.

The president also seemed to signal some leeway on revenues. He declined to rule out raising the income threshold above his last offer of $400,000. Boehner wants it to remain at $1 million.

Obama drew a hard line against negotiating around the debt limit, saying he would not allow Republicans to use it as a leverage point to gain more spending cuts.

“I will not negotiate around the debt ceiling,” Obama said. “We’re not going to play the same game that we saw happen in 2011, which was hugely destructive.”

The administration officially responded to the Plan B strategy Wednesday by issuing the veto threat. Administration officials said they were confounded by Boehner’s strategy of putting a bill on the House floor that fails to deal with many of the items most important to his members while asking them to break their party’s no-taxes pledge.

“The deficit reduction is minimal, and perversely, given its authors, solely through tax increases with no spending cuts,” White House communications director Dan Pfeiffer said in a statement. “This approach does not meet the test of balance, and the president would veto the legislation in the unlikely event of its passage.”

Brendan Buck, Boehner’s press secretary, called the threat “bizarre and irrational.”

“The White House’s opposition to a back-up plan to ensure taxes don’t rise on American families is growing more bizarre and irrational by the day,” Buck said in an emailed statement. “Republicans have always said a broader, ‘balanced’ plan is the ideal solution, and we have put one forward. In the absence of a ‘balanced’ solution from the President, however, we must act to stop taxes from rising across the board in 12 days. If Democrats disapprove of this bill, then there is a simple solution: amend it in the Senate and send it back to the House.”

Obama is scheduled to travel to Hawaii on Friday for a family vacation but will remain in Washington until Congress’s schedule comes into focus, the officials said.