In a short press conference during which he did not take questions, House Speaker John Boehner effectively rejected Obama's new fiscal cliff proposal.
Boehner was responding to Obama's comments earlier Wednesday expressing his frustration that a comprehensive fiscal cliff deal has yet to be reached, saying the President's suggested plan is "far from a balanced approach."
Nancy Pelosi is expected to comment on the continuing back-and-forth about the impending expiration of Bush-era tax cuts and how to avoid plunging the US back into a recession.
"We should be able to get this done, we need to get this done, and we don't have a lot of time," the president said in comments following his announcement about the White House's gun control task force.
His comments come in the shadow of Boehner's so-called "Plan B," which discouraged higher taxes on incomes below $1 million.
"I'm in that income bracket, I'd love to pay less taxes, but this is the right thing to do," said Obama. "This is not a situation where I'm willing to compromise."
More from GlobalPost: Fiscal cliff: Obama rejects Boehner's 'Plan B' (UPDATE)
Obama said he was open to spending cuts, but that he would not back down on taxing America's wealthiest citizens nor would he negotiate the debt ceiling.
"If this past week has done anything, it should give us some perspective about what's important," Obama said, referring to the shooting in Newtown, Connecticut.
"I would like to think that members of that caucus would say, we disagree with the president on a whole bunch of things ... but right now, what the country needs is for us to compromise ... and make sure we're laying the foundations for growth."
"This is the United States of America, the greatest economic superpower," said Obama. "And the idea that we lurch from crisis to crisis, threatening not to pay our bills on stuff we've already paid for, is not [the way it should be.] I will not compromise on this."