Cantor, R-Virginia, told reporters after Wednesday's meeting that he proposed a short-term agreement to raise the federal debt ceiling, a position Obama has previously rejected.
"That's when he got very agitated and said I've sat here long enough -- that no other president -- Ronald Reagan -- would sit here like this -- and that he's reached the point that something's gotta give," Cantor said, adding that Obama called for Republicans to compromise on either their insistence that a debt-ceiling hike must be matched dollar-for-dollar by spending cuts or on their opposition to any kind of tax increase.
"And he said to me, 'Eric, don't call my bluff.' He said 'I'm going to the American people with this,' " Cantor quoted Obama as saying.
"I was somewhat taken aback," Cantor said. When he continued to press the issue, Cantor said, Obama "shoved back from the table, said 'I'll see you tomorrow' and walked out."
A Democratic source familiar with the talks said on condition of not being identified that Obama cut off Cantor at the end when the Virginia Republican questioned the president for a third time on his opposition to a short-term extension of the federal debt ceiling.
Another Democratic source, also speaking on condition of anonymity, described the tone of the meeting as tense but constructive and said that at one point, Cantor was challenged on what the source called "talking out of both sides of his mouth."
Obama has insisted on one deal that will raise the amount of money the government can borrow to sufficient levels to last through 2012 -- after his campaign for re-election. Cantor's call for a short-term agreement also could win the support of House Speaker John Boehner, R-Ohio, an aide to Boehner said.