"As the gentleman knows, organized labor in this country is very supportive of that bill," Cantor said of the oil pipeline language. "It means immediate jobs. The president continues to say he is for creating jobs, doing all we can to get American back to work. This is a provision that allows for that.

"Knowing that there is strong bipartisan support for the project, knowing that labor is in support of it, knowing that it puts people back to work immediately, it would seem to me that this is a consistent provision to go along with making sure that we deal with the unemployment situation in this country," Cantor added.

House Republicans have not unveiled their bill yet, but announced today they would propose a bill to extend and reform unemployment insurance, extend the soon-to-expire payroll tax and deal with the reimbursement rate for Medicare physicians. Republicans added language on the Keystone pipeline and a provision delaying the Environmental Protection Agency's industrial boiler regulation as incentives to get GOP support.

Hoyer tried unsuccessfully to convince Cantor to drop the Keystone language, by arguing that House Speaker John BoehnerJohn Andrew BoehnerJohn Feehery: A political forest fire Trump's pick for Federal Reserve chief is right choice at right time The two-party system is dying — let’s put it out of its misery MORE (R-Ohio) has promised to deal with bills "one issue at a time," not by putting riders on must-pass bills.

"It seems inconsistent when the president of the United States yesterday said he would veto such a provision that we would include it in legislation that is 'must-pass,' " Hoyer said.

Hoyer also noted press reports that said Republican Study Committee Chairman Jim Jordan (R-Ohio) supports the GOP proposal in particular because Obama opposes it.

"It seems to me that if you're serious … that we not include in that bill an item that apparently is popular on your side just because the president doesn't like it, according to Mr. Jordan," Hoyer said.