The vote suggested that a period of political warfare between G.O.P. factions would continue to shape lawmaking in the state.

A push by Texas' hard right to widen control in the state Capitol fell short Tuesday after House lawmakers rejected its choice for the powerful speakership amid a Republican feud accelerated by the historic impeachment of Attorney General Ken Paxton.

The new speaker will have a dramatic impact on the direction of this year’s lawmaking — and potentially the future of the Legislature.

After current House Speaker Dade Phelan dropped his bid to keep the gavel in early December, one member of his leadership team, Representative Dustin Burrows of Lubbock entered the race pitting himself against Representative David Cook of Mansfield.