Another member of the state's congressional delegation — Rep. Joe Barton (R-Texas) — said earlier this week that he's also looking at the race. But Barton indicated he was unlikely to get in if Dewhurst decides to run. 

"It's a possibility, but I wouldn't say it's a probability," Barton said of a Senate bid, acknowledging how tough it is to run statewide in Texas from a House seat.

"We have 32 congressional districts in Texas, so anyone who has already run statewide has a built-in advantage," said Barton. "Now, if you're from one of the major metropolitan areas and have pretty good name ID, which I do, it's a little easier. But it's still tough."  

Rep. Ron Paul (R-Texas) said his interest was piqued by a poll from Democratic-leaning Public Policy, which showed he was the pick of 20 percent of Texas Republicans, second only to Dewhurst, who polled at 23 percent. 

While conceding that a run has "certainly crossed my mind," Paul didn't make a Senate bid sound likely, adding, "It's crossed my mind before, so I don't know that it means much." 

One thing McCaul would have is the ability to put some of his own money into a Senate race should he decide to get in.

Railroad Commissioner Michael Williams resigned his seat on the commission this week to concentrate on a Senate run, and former Solicitor General Ted CruzTed CruzCruz defends Trump's Taiwan call Ark., Texas senators put cheese dip vs. queso to the test Pentagon's suppressed waste report only tip of the inefficient machine MORE, former Secretary of State Roger WilliamsRoger WilliamsNew House GOP campaign chairman starts with a lead GOP votes to keep Ryan as Speaker Lawmakers suggest Wells Fargo chief should face criminal charges MORE and Railroad Commissioner Elizabeth Ames Jones are also officially in the race.