The last-minute Senate challenge this week by outspoken Texas GOP Rep. Steve Stockman is generating strong reaction but only a lukewarm response from the influential conservative groups he will likely need to win.

Stockman’s unexpected filing Monday to take on incumbent Texas Sen. Jon Cornyn had the liberal media scrambling to compile lists of his bomb-throwing antics. However, the announcement also caught conservative groups by surprise, with some suggesting the timing and other factors will keep them on the sidelines for this GOP primary.

“While Congressman Stockman has a pro-economic growth record, so does Senator Cornyn, as witnessed by his 87 percent lifetime Club for Growth score,” said Chris Chocola, president of the group's political action committee.

Chocola said the fiscal conservative group -- known for daring to jump into GOP primaries -- considers three factors before putting money into a race: the strength of the incumbent’s record, the viability of the challenger and the degree of difference between the candidates on economic issues.

The well-funded group is already supporting the primary challenger in Mississippi Republican Sen. Thad Cochran’s re-election bid.

As a measure of the group’s power, the Club for Growth spent at least 8 million in the 2010 wave election that helped Republicans retake control of the House, with 20 of its 26 general-election candidates winning their congressional races.

Stockman, who served one House term in the mid-1990s and was elected again in 2012, is perhaps best known for raffling a Bushmaster rifle this summer, calling for President Obama to be impeached and last year inviting zany, gun-loving rocker Ted Nugent to the president’s State of the Union address.

Despite the Club for Growth and similar groups arguing the Texas primary is just three months away, leaving them little time to assess the situation, Cornyn, the No. 2 Republican in the Senate, also has nearly $7 million in his campaign cash, compared to roughly $32,000 for Stockman, further decreasing the odds of a Stockman upset.

Until this week, Cornyn, the Senate's minority whip, appeared to have escaped a major primary challenge from the Tea Party or other conservative factions, despite facing a handful of lesser-known primary challengers.

The groups FreedomWorks and Senate Conservatives Fund reportedly are still considering whether to back Stockman.

Stockman was elected to a district outside Houston last year after a low-profile campaign in which he largely ignored the media but urged voters to support his "re-election."

His first House term started in 1994, and he perhaps is even better known for accusing the U.S. government of "executing" members of the Branch Davidian cult after the siege near Waco.

Cornyn has been endorsed by Texas GOP Gov. Rick Perry and should remain the race's clear favorite.

Though he insists he's one of the most conservative members Congress, Cornyn has drawn the ire of some grass-roots groups for not being enough like Texas' junior senator, Tea Party firebrand Ted Cruz, who led a conservative-backed campaign this summer and fall to “defund” ObamaCare.

"Senator Cornyn looks forward to discussing his conservative record with Texans," Cornyn campaign manager Brendan Steinhauser said in response to Stockman's filing.

Cornyn now faces seven primary challengers, with five Democrats in that party's primary.

The Associated Press contributed to this report.