Durbin -- the second-ranking Democrat in the Senate -- said on his Facebook page the Republican, who he did not name, made the disrespectful remark to Obama during negotiations with the White House during the federal budget standoff.
Asked about it during Wednesday's regular daily briefing with reporters, White House spokesman Jay Carney said, "It did not happen."
Carney said he had discussed the claim with a "participant in the meeting," The Hill reported.
"Senator Durbin stands by his comments," Durbin spokesman Max Gleischman said.
"Many Republicans searching for something to say in defense of the disastrous shutdown strategy will say President Obama just doesn't try hard enough to communicate with Republicans," Durbin initially said on Facebook. "But in a 'negotiation' meeting with the president, one GOP House Leader told the president: 'I cannot even stand to look at you.'
"What are the chances of an honest conversation with someone who has just said something so disrespectful?" he said.
Republicans have denied a GOP lawmaker made such a remark.
Brendan Buck, a spokesman for House Speaker John Boehner, R-Ohio, said in a statement Durbin's accusation "is a serious one, and it appears to have been invented out of thin air."
"The senator should disclose who told him this account of events, retract his reckless allegation immediately, and apologize," Buck said.
Durbin's office did not immediately respond to The Hill's request for comment.