House Speaker John Boehner's office is working with the Rules Committee to craft the resolution that would determine the contours and function of the select committee to investigate the deadly 2012 attack on the U.S. consulate in Benghazi, Libya.

The resolution could receive a Rules Committee hearing on Wednesday and hit the House floor for consideration Thursday or Friday, Republican sources confirmed Monday after Boehner, R-Ohio, announced that he was appointing Rep. Trey Gowdy, R-S.C., chairman of the select committee. Boehner, who holds the power to appoint all members of the select committee, plans to name some Democrats to the panel unless they choose to boycott.

The select committee’s staff could number about 20, with aides drawn from the five standing House committees of jurisdiction that have until now worked jointly to investigate the Sept. 11, 2012, terrorist attack on the U.S. diplomatic compound in Benghazi that left four Americans dead, including Ambassador Christopher Stevens. Those committees are Armed Services, Foreign Affairs, Intelligence, Judiciary and Oversight and Government Reform.

Staff hires from the private or think-tank sectors also are possible.

“I plan to ensure he and his committee have the strongest authority possible to root out all the facts,” Boehner said as a part of a statement announcing Gowdy’s appointment.

Still not clear is how many members the select committee will have. But those appointed could be drawn from the panels that have been handling the existing investigation, or from an informal committee of Republicans that has been meeting once a week to monitor the joint investigation. Rep. Lynn Westmoreland, R-Ga., who serves on the House Intelligence Committee, has been chairman of the informal committee and could make the cut.

Westmoreland told the Washington Examiner on Monday that he is interested in serving on the committee. The members who served on his informal Benghazi committee included Gowdy; Devin Nunes of California; Jason Chaffetz of Utah; Mike Conaway of Texas; Tom Cotton of Arkansas; Jim Gerlach of Pennsylvania; Joe Heck of Utah; and Adam Kinzinger of Illinois.