California Republican Kevin McCarthy is the clear favorite to replace departing House Majority Leader Eric Cantor.
McCarthy is currently the Majority Whip, the number three post in the GOP leadership chain.
Key challengers to McCarthy have dropped out as Republicans prepare to vote on leadership posts next week.
Cantor will step down as majority leader at the end of July after being defeated in a primary election race in Virginia.
He will serve out the remainder of his congressional term, which concludes at year's end.