House Majority Leader Eric CantorEric Ivan CantorFeehery: The governing party 'Release the memo' — let's stop pretending that Democrats are the defenders of the FBI Raúl Labrador, a model for Hispanic politicians reaching higher MORE (R-Va.) late Monday called on Democrats to “do the right thing” and join the select committee to investigate the Benghazi terrorist attack.

Cantor confirmed for Fox News’s “On the Record” that the House will vote this week on the formation of the select committee.

"There will be a vote this week to form this committee going forward. And I know that Chairman Gowdy, a terrific and serious legislator, is going to it do a great job in leading this effort," Cantor said.

He did not specify which day the vote would be held.

House Democratic Whip Steny Hoyer (D-Md.) said Monday that he would urge members of his caucus to vote against the formation of the committee.

Rep. Adam Schiff (D-Calif.) has also suggested Democrats should boycott the committee.

The White House suggested on Monday it might not cooperate with the committee’s activities.

Cantor said the select committee, to be headed by Rep. Trey Gowdy (R-S.C.), would likely have a time frame for its probe.

"I think that the resolution that will be creating this select committee will state very clearly with the mission is and a time to us to wrap things up with some takeaways."

On Monday, Rep. Pete King (R-N.Y.) said the committee should complete the inquiry by the 2016 presidential election.