Sen. Ted Cruz (R-TX), who himself was catapulted by tea party support to win a Texas Senate seat, has said he is unlikely to endorse in primary races.
Texas Gov. Rick Perry (R) has already endorsed Cornyn.
Rep. Louie Gohmert (R-TX) said he does not plan to endorse in the primary.
Texas Attorney General Greg Abbott (R), who seems poised to be the next governor of Texas, will reportedly not endorse in the primary.
Rep. Blake Farenthold, a tea party favorite in Texas, in an interview with the Dallas Morning News, refrained from taking a side in the race.
"If you're going to play, play big, and Steve's playing big," Farenthold said to the Texas newspaper. "The voters in Texas will have the opportunity to sort it out."
In interviews with The Hill both Reps. Kay Granger (R-Texas) and Kenny Marchant (R-Texas) said they wouldn't be endorsing Stockman. Marchant said he didn't see "Cornyn losing. Cornyn has done a great job for us." Granger endorsed Cornyn.
The Club for Growth, which has made its fair share of endorsements of tea party challengers, announced shortly after Stockman jumped into the race that it would not endorse in the primary.
The Senate Conservatives Fund, one of the most prominent conservative outside groups that aims to replace incumbent Republicans with more conservative lawmakers, held back from an endorsement.
"We haven't decided yet whether we will endorse Steve Stockman, but we're glad he's running," Senate Conservatives Fund Executive Director Matt Hoskins said in a statement to TPM. "Texas deserves two conservative fighters in the Senate, not just one. John Cornyn has voted to increase the debt, raise taxes, bail out Wall Street banks, and fund Obamacare. He's part of the problem in Washington and voters deserve a choice."
Likewise the conservative Madison Project, another outside group that regularly endorses conservative challengers, did not endorse Stockman.
"Stockman definitely is conservative, not just in votes but in voice," The Madison Project's Daniel Horowitz told Politico. "However, because this whole thing took us by surprise, we haven't met with him or assessed him as a potential Senate candidate." According to Horowitz, "it would be hard to find enough money to run statewide in just three months."
FreedomWorks was less direct but hardly made an endorsement.
"We have to admit Congressman Stockman's entry took us by surprise. We're taking a close look at his record now," FreedomWorks's Dean Clancy said also according to Politico. "I can't say yet whether we'll endorse in this race, but I am certain we won't be endorsing the incumbent, Senator Cornyn, in 2014."
And the Chamber of Commerce not only passed on Stockman after he announced his candidacy, it endorsed Cornyn instead.
"Senator Cornyn is a conservative champion for the American free enterprise system. He has a proven record on issues important to the business community and has received a 90 percent lifetime voting record with the U.S. Chamber," Chamber National Political Director Rob Engstrom said in a statement according to The Hill. "The Chamber is proud to stand with him."