WASHINGTON — The House Republican leadership, so solid in its opposition to President Obama, was torn apart Tuesday by the defeat of its most influential conservative voice, Representative Eric Cantor, the House majority leader. His demise will reverberate all the way to the speaker’s chair, pull the top echelons of the House even further to the right and most likely doom any ambitious legislation, possibly through the next presidential election.

Conservatives who have helped fuel some of the most contentious showdowns over the last three years on issues such as immigration and raising the federal debt ceiling are likely to be emboldened by Mr. Cantor’s shocking loss as they seek to replace him with someone even more closely aligned with their views.

Further, House Republicans began to immediately plot a new leadership structure that before Tuesday night had hinged merely on whether Speaker John A. Boehner would seek to keep his post next year.