Chris Cillizza talks to the Texas Tribune’s Evan Smith about Sen. John Cornyn’s surprise primary challenge from a congressman “on the outer edge of the outer edge.” (The Washington Post)

More than half of Senate Republicans facing reelection next year face potentially viable tea party challenges — a historically large threat to the GOP establishment that could, once again, kill the party’s chances of taking back control of the chamber.

A surprise challenge to Sen. John Cornyn, the No. 2 GOP leader, emerged at the last minute before Texas’s election filing deadline late Monday, and on Tuesday a conservative group with deep pockets threw its financial support behind a radiologist, who has never run for office, in a primary against Sen. Pat Roberts (Kan.), a 16-year veteran.

Many of the upstarts are considered long shots, and some are in states that are so deeply conservative that even a gadfly Republican would be likely to win in the general election. But a similar situation has tripped up Republicans in the past two elections, costing them seemingly winnable seats in states such as Nevada, Missouri and Indiana.

Moreover, in a year in which the electoral map and President Obama’s sagging poll numbers provide Republicans their best opportunity to win back the Senate in a decade, GOP veterans are increasingly frustrated by the amount of time, energy and cash that will be spent trying to deal with internal feuds.

“They’re really undermining everything we’re trying to do here,” Sen. Orrin G. Hatch (R-Utah), who stands to chair the powerful Finance Committee if Republicans win the majority, said of the independent groups that are providing financial and other support for the challengers. The path to conservative victories is through defeating Democrats, Hatch said. “You can’t do it by destroying sitting [GOP] senators.”

Senate Republican primary challenges

Conservative activists, how­ever, say their goal is to remake the Republican Party from the outside, focusing their efforts particularly on red-leaning states where the incumbent is in­sufficiently strident in opposing Obama and Democrats.

“All we want to do is pass a fiscally conservative agenda through the Senate,” said Barney Keller, spokesman for the Club for Growth, which is the best-funded conservative outlet and is backing the challenger to Sen. Thad Cochran (R-Miss.), who was first elected in 1978.

Several of the insurgents seized on a modest two-year bipartisan budget deal announced Tuesday evening, saying they opposed it because it raises spending too much.

Aside from just challenging incumbents, groups such as the Club for Growth also hope they can push sitting senators further to the right. By helping defeat Sen. Robert F. Bennett (R-Utah) in 2010, for instance, the Club for Growth says, it scared other GOP incumbents.

“We got Orrin Hatch to vote a pro-growth agenda for two years,” Keller said.

Republicans need to pick up six seats to win the majority, while Democrats are defending 21 seats, including seven key Senate battlegrounds in places where Obama lost in 2012. That margin would be much smaller if not for a series of GOP candidates who emerged from ideological primaries in 2010 and 2012 as tea party heroes, only to blunder through the general election and lose winnable races.

Seven of the 12 Republicans running next year face tea party challengers.

“People are no longer deferential to existing officeholders,” said Stuart Rothenberg, editor of the independent Rothenberg Political Report. “We’ve entered a whole new era. I’ve never seen anything like it before.”

Some veterans suggested that the remedy for discouraging primary challenges was aggressive campaigns that throttle opponents, such as in Hatch’s 2012 primary contest against a tea party opponent, as opposed to weak campaigns like that of longtime incumbent Sen. Richard G. Lugar (R-Ind.), who lost in 2012.

“The only cure for political ambition is embalming fluid,” said Sen. Johnny Isakson (R-Ga.).

Isakson is up for reelection in 2016 in Georgia, where tea party challengers popped up even before Sen. Saxby Chambliss (R-Ga.) announced he would not run for reelection next year. Big victories in 2014 over these challengers, Isakson said, “would certainly slow down the drive to do it.”

Sen. John McCain (R-Ariz.), who weathered a tea party challenge in 2010, less than two years after serving as the GOP presidential nominee, said he has given his colleagues facing primaries specific instructions: “Play offense. Go after your opponent. Your opponent’s going after you, you go after your opponent. The best defense is a good offense.”

To that end, Cochran, 76, whose last tough campaign was more than three decades ago, is hosting a big $1,000-per-person fundraiser Wednesday at a Capitol Hill townhouse, declaring it an “ALL HANDS ON DECK” event on the invitation.

The National Republican Senatorial Committee, the GOP’s campaign arm, remains confident that the incumbents will win and next year’s focus will be on Obama’s health-care law. “All of our Republican incumbents are well prepared and equipped to run successful campaigns,” said Brad Dayspring, NRSC spokesman. “We will bring them all back.”

Republicans had a plan to avoid these bruising primaries. Senate Minority Leader Mitch McConnell (R-Ky.), who is also facing a primary challenge from a businessman who has never held office, appointed Sen. Ted Cruz (R-Tex.) as vice chairman of the NRSC. Cruz was originally slated to be the liaison to outside conservative activists, having become a tea party icon with his upset victory in 2012 over David Dewhurst, the powerful Texas lieutenant governor.

Rather than mollifying those outside groups, Cruz devoted much of his political work to helping their cause and raising money for them, particularly the Senate Conservatives Fund. That group endorsed Roberts’s opponent Tuesday and voiced support for the surprise campaign of Rep. Steve Stockman (R-Tex.) against Cornyn. The fund is already backing McConnell’s opponent, businessman Matt Bevin.

“Nearly every incumbent usually gets a very nominal challenger, but this is the first cycle I remember where so many incumbents have challengers with the potential to run credible races,” said Jennifer Duffy, senior editor for the nonpartisan Cook Political Report, where she has analyzed Senate races for 25 years.

It remains to be seen whether enough resources exist to fund each of the challenges. The Club for Growth has been the most discerning in its financial support over the years, backing only candidates it thinks have legitimate chances of winning. It steered more than $6 million toward Cruz in 2012 but dismissed Stockman on Tuesday by saying that Cornyn was sufficiently conservative.

Stockman, a one-term congressman in the mid-1990s, won election in 2012 and promptly joined a rump caucus of two dozen or so House conservatives in frequently challenging the GOP leadership. While that is the normal requisite to win support from groups such as the Club for Growth and the Senate Conservatives Fund, Stockman has a history of making controversial remarks. He accused the Clinton administration of staging the 1993 raid in Waco, Tex., to pass an assault-weapons ban and has a spotty record in his personal businesses.

Still, Cornyn said he saw what Cruz did in 2012 and does not intend to take lightly the challenge from Stockman or any of the other candidates running against him.

“Obviously there are lessons to be learned from that,” he said. “And, believe me, I’ve learned them.”