Speaker John Boehner (R-Ohio) and House Majority Leader Eric Cantor (R-Va.) met with President Obama on Sunday to discuss the debt-ceiling impasse.

A spokesman for Boehner said the meeting was held simply to keep the lines of communications open between House leaders and the White House. 

"As we said throughout the weekend, the lines of communications are being kept open. But there is nothing to report in terms of an agreement or progress,” Boehner spokesman Kevin Smith said in a statement. 

House Republicans still intend to hold a vote Tuesday on the conservative-backed “Cut, Cap and Balance” package that would tie passage of a balanced-budget amendment to a $2.4 trillion increase in the federal debt limit.

“We believe cut, cap and balance represents the best path forward, and we are looking forward to the House vote on it tomorrow," Smith said.

The White House on Monday warned that Obama would veto the "Cut, Cap and Balance" bill, calling it an “empty political statement.”

The legislation is likely to pass the House, but is expected to go down to defeat in the Senate.