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 CruzTrump enters new debate frontier Pence offers Cruz 'heartfelt thanks' for Trump endorsement Cruz: Trump hasn't apologized for personal insults MORE, former Secretary of State Roger WilliamsRoger WilliamsNY rep swipes at Kaepernick after NYC bombing suspect caught Overnight Regulation: House bill to block Obama regs advances Lawmakers launch Congressional Football Caucus MORE and Railroad Commissioner Elizabeth Ames Jones are also officially in the race.