John Cornyn

Sen. John Cornyn at his reelection campaign kickoff rally in Austin, Texas, last month. (Rodolfo Gonzalez / Austin American Statesman / November 15, 2013)

WASHINGTON - Mitch McConnell isn't the only Republican Senate leader who must contend with a noteworthy primary challenge.

Sen. John Cornyn of Texas, the Republican whip, will face a conservative challenger in Rep. Steve Stockman (R-Texas), who submitted paperwork late Monday for the March primary.

Stockman, who returned to Congress this year after serving a single term in the 1990s, had been planning to run for reelection. An aide filed the application just 15 minutes before the close of the state filing period, the Houston Chronicle reported.

It's unclear how serious a challenge Stockman can mount in a short campaign in one of the nation's most populous states. Texas' March 4 primary is the earliest in the nation, and Stockman's campaign account is in debt. Cornyn, a two-term senator, had nearly $7 million on hand at the end of the most recent fundraising period.

But Stockman will seek to rally grass-roots conservatives to his campaign against Cornyn, the second-ranking Senate Republican and a former chairman of the Senate Republicans' campaign committee. In an interview with the conservative website World Net Daily, Stockman accused Cornyn of siding with President Obama against fellow Texas Sen. Ted Cruz in the recent unsuccessful fight to defund Obamacare.

PHOTOS: The battle over Obamacare

"He needs to be held accountable for his decisions," Stockman said.

Cruz led an effort by conservative activists to strip funding for the Affordable Care Act in budget negotiations, a stance that resulted in a 16-day government shutdown and nearly risked defaulting on the nation's bills.

Public opinion polls showed the Republican Party took the brunt of the blame for the shutdown.

Stockman has made several headline-seeking moves since returning to Washington, most notably inviting rocker and conservative activist Ted Nugent to attend the State of the Union address in the House gallery.

Two other lesser-known Republicans have also filed to challenge Cornyn.

McConnell faces a serious threat in Kentucky's May primary from Matt Bevin, a businessman who has been endorsed by the Senate Conservatives Fund and other tea party groups. Republican incumbents in South Carolina, Wyoming and Mississippi also face credible primary challenges.

michael.memoli@latimes.com

Twitter: @mikememoli