Barton said the open Senate seat is naturally a draw for most members of the delegation, but said the reality is that a House seat in Texas isn't the easiest launching pad for a Senate bid. 

"We have 32 congressional districts in Texas, so anyone who has already run statewide has a built-in advantage," he said. "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." 

Barton made national headlines last year after he apologized to BP CEO Tony Hayward in the midst of the Gulf oil spill for what he called a "shakedown" on the part of Obama administration. Barton later retracted his apology. 

The Republican field in the open seat Senate contest is already a crowded one. 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 CruzDebbie Wasserman Schultz marks 10 years as breast cancer survivor Foreign agent registration is no magical shield against Russian propaganda Let Trump be Trump and he'll sail through 2020 MORE, former Secretary of State Roger WilliamsJohn (Roger) Roger WilliamsThe Hill's Whip List: Where Republicans stand on tax-reform bill Overnight Finance: Freedom Caucus chair courts Dems on tax reform | House passes .5B disaster relief package | House GOP worries about budget's fate in Senate 69 Republicans vote against aid for Puerto Rico, other disaster sites MORE and Railroad Commissioner Elizabeth Ames Jones are also all officially in the race. 

Sen. Jim DeMint (R-S.C.) served notice last week that he would likely wade into the primary by making an endorsement. In an email to supporters of his Senate Conservatives Fund, DeMint talked up Michael Williams and Ted Cruz and took an early shot at Dewhurst, labeling him the "establishment" candidate. 

Barton said it was a label that doesn't fit Dewhurst and one that he's confident won't stick if the Lt. Gov. enters the race. 

"I don't know anyone that's saying that," Barton said. "David's a good man and he's a strong conservative."