"Republicans in Congress face a simple choice: Are they willing to compromise to protect vital investments in education and health care and national security and all the jobs that depend on them? Or would they rather put hundreds of thousands of jobs and our entire economy at risk just to protect a few special interest tax loopholes that benefit only the wealthiest Americans and biggest corporations?" he asked. "That's the choice."

"This is not an abstraction," he said. "People will lose their jobs."

Tuesday morning, the Wall Street Journal reported the existence of a new potential basis for compromise: Alan Simpson and Erskine Bowles, who penned the failed Simpson-Bowles plan for reducing the deficit, are working on a new proposal that would reform the tax code and implement deep spending cuts.

According to the Wall Street Journal, that plan would reduce the deficit by $2.4 trillion over 10 years, identifying $600 billion worth of cuts through reforms to entitlement programs, and $600 billion worth of revenues by closing various tax loopholes.

House Speaker John Boehner, however, has dismissed the idea of raising taxes in any way, and argued in a statement responding to Mr. Obama's remarks that the only way to replace the sequester is to pass "a plan to cut spending that will put us on the path to a balanced budget in 10 years."

"To keep these first responders on the job, what other spending is the president willing to cut?" he asked.