Tea Party groups' ire centers on Cornyn's decision in late July to remove his signature from a letter by Sen. Mike Lee (R-UT) expressing strong support to defund Obamacare in any debt limit or government funding bill. Cornyn was one of a number of senators who had originally signed the letter a few days before he changed his mind and removed his signature.
At the time, Cornyn's office said the senator supports defunding Obamacare but not at the risk of a government shutdown. Cornyn's office maintains that he has been fighting "tooth and nail" against Obamacare. Cornyn spokesman Drew Brandewie noted that the senator was one of the original cosponsors of Sen. Ted Cruz's (R-TX) original bill to defund Obamacare.
But that's not enough for the tea party crowd.
"Senator Cornyn says he opposes Obamacare and he even says he support defunding Obamacare, but he won't pledge to oppose funding for Obamacare when it comes up for a vote in September," Matt Hoskins, executive director of Senate Conservatives Fund, told TPM in an email.
The Senate Conservatives Fund, which was founded by former Sen. Jim DeMint (R-SC), has hit a number of Republicans for what the group argues is insufficient or wavering opposition to Obamacare. The group does not endorse incumbents and, therefore, won't endorse Cornyn, who is up for re-election in 2014.
"This is when conservatives need him. He voted for the FY2013 CR earlier this year, which also included funding for Obamacare. If people in Texas don't make their voice heard, he will vote to fund it again," Hoskins added.
"After reviewing the letter, Sen. Cornyn decided the best approach was Sen. Cruz's bill, since a government shutdown will still fund most of Obamacare," Brandewie told TPM on Thursday. "Sen. Cornyn voted against Obamacare repeatedly before it became law and he's voted to fully defund and repeal it every time it's come up for a vote."
On Wednesday, representatives of Tea Party groups participating in a multistate anti-Obamacare "Exempt America Tour" gathered in Austin, Texas, to urge Cornyn to "join the fight" and support a debt limit or government funding bill only if such a proposal includes defunding Obamacare. Participants at the event included members from Tea Party Patriots and the conservative online movement ForAmerica.
"He is one of those who has been so outspoken in his opposition to this," Brent Bozell, the chairman and co-founder of For America said at the event according to the Texas Tribune. "He has spent so much time telling the voters of Texas how he was doing everything in his power to put an end to it. So far, he's ducking."
Hoskins echoed Bozell's argument.
"If he is opposed to Obamacare, he shouldn't vote to fund it," Hoskins added to TPM. "If he truly wants to stop the law from being implemented, this is the last chance to do that. He has voted against government funding bills before. Why won't he vote against one that includes money for Obamacare?
"Senator Cornyn knows that defunding Obamacare is the right course of action. It's why he originally signed Mike Lee's letter. But he withdrew his name because Mitch McConnell asked him to. Voters in Texas want Senator Cornyn to know that he works for them, not Mitch McConnell."
Cornyn so far has not drawn a strong Tea Party challenger to his re-election. Tea Party groups have urged Rep. Louie Gohmert (R-TX) to challenge Cornyn, but Gohmert shot down the idea telling the Washington Examiner "it's not on my radar." Cornyn is wary of challenge from his right flank and followed the playbook of a number of incumbent Republicans by hiring a Republican with a background in the Tea Party movement to help run his campaign. In July Cornyn brought on Brendan Steinhauser, formerly the director of campaigns for FreedomWorks, to serve as campaign manager.
"We're going to take the primary seriously," Steinhauser told the Houston Chronicle. "We're going to work very hard. We're not going to take any voter for granted."
For his part, Cornyn wrote an op-ed earlier this month at National Review touting his early opposition to Obamacare: "I voted against Obamacare four years ago, and I strongly support replacing the entire thing with patient-centered reforms that actually address America's biggest health-care challenges."