His decision takes pressure off Minority Leader John Boehner (R-Ohio) and ratchets it up for Minority Whip Roy Blunt (R-Mo.), who brought Cantor into the leadership circle when he selected him as his deputy six years ago.

“Mr. Blunt is focused right now on speaking to members of the House Republican Conference that have reached out to him, and in doing what is best for the future of the Republican Party and the nation,” said spokeswoman Antonia Ferrier.

Cantor was widely thought to be the only member capable of mounting a significant challenge to Boehner to lead the House GOP. But Cantor has apparently decided he stands a better chance to take over Blunt's position.

Cantor spokesman Rob Collins said that Cantor and Blunt had a discussion Wednesday morning, but declined to describe the nature of the conversation. 

Collins added that Cantor, following his discussion with Blunt, called members of the Republican Conference to express his interest in the position. 

Asked why he decided against challenging Boehner, Collins said, "Eric has been the Number Two whip for six years; it's a natural progression." 

Should he opt not to run for whip, Blunt would be the second member of GOP leadership to leave following the loss of at least 19 seats in the House. Conference Chairman Adam Putnam (R-Fla.) announced late Tuesday night he would not seek a second term. 

Republican Study Committee Chairman Jeb Hensarling will run to replace Putnam, sources close to the Texas Republican said on Wednesday.

Other leadership races have begun to shape up farther down the ticket. Rep. Michael Burgess (R-Texas) announced Wednesday he would challenge Policy Chairman Thaddeus McCotter (R-Mich.).

National Republican Congressional Committee Chairman Tom Cole (Okla.) also announced he would seek reelection to his post. He will be challenged by Rep. Pete Sessions (R-Texas).

House Republicans will meet Nov. 17 to discuss the leadership structure of the party going forward into the 111th Congress.