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."  

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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 CruzRafael (Ted) Edward CruzThe Hill's Morning Report - Presented by the Air Line Pilots Association - Negotiators 'far apart' as talks yield little ahead of deadline Wary GOP eyes Meadows shift from brick-thrower to dealmaker Trump-backed Hagerty wins Tennessee GOP Senate primary MORE, former Secretary of State Roger WilliamsJohn (Roger) Roger WilliamsThe Hill's 12:30 Report - Presented by Facebook - Yoho apologizes for accosting AOC Ocasio-Cortez accosted by GOP lawmaker over remarks: 'That kind of confrontation hasn't ever happened to me' Cook shifts 20 House districts toward Democrats MORE and Railroad Commissioner Elizabeth Ames Jones are also officially in the race.