The president said Republicans should "peel off the war paint" and take the deal he is offering.
The latest White House offer would extend the Bush tax cuts for every American earning less than $400,000 a year. Boehner's plan would extend the Bush tax cuts for everybody making less than $1 million.
Mr. Obama threatened to veto a bill drafted by House Republicans, but Boehner quickly responded, saying the president would be responsible for the "largest tax increase in history" if he makes good on that threat.
"The president promised the American people a balanced approach. And I hope the president will get serious soon about providing and working with us on a balanced approach," Boehner said.
A house vote is set for Thursday, but it's unlikely that the legislation will get far. Boehner expressed confidence the Republicans' narrow so-called Plan B bill would clear the House, but a cold reception awaits in the Democratic-controlled Senate.
The Internal Revenue Service warned that the fiscal cliff could delay tax filings. Up to 100 million taxpayers won't be able to file their tax returns until late March if lawmakers don't adjust the alternative minimum tax by the end of the year.
On paper, the two sides are relatively close to an agreement on major issues, each having offered concessions in an intensive round of talks that began late last week. But political considerations are substantial, particularly for Republicans.
The Associated Press contributed to this report.