WASHINGTON -- Rep. Steve Stockman's moment as a viable Senate candidate lasted exactly 13 hours 47 minutes.

At 7 p.m. Monday, the far-right Stockman, R-Toxicity, announced via the right-wing website WND that he would challenge incumbent John Cornyn in the Texas Republican Senate primary. And for a brief period, it appeared that Stockman could pose a credible threat; his decision was immediately praised by the tea-party patriots and the Senate Conservatives Fund, founded by the Heritage Foundation's Jim DeMint.

But then something unexpected happened: Sanity prevailed.

The Club for Growth, which started the trend of conservative primary challenges to incumbent Republicans, issued a statement just before 9 a.m. Tuesday saying that it was not on board with Stockman, the flamboyant lawmaker who distributed articles of impeachment against President Obama this fall and who tweets messages such as "Obamacare is less popular than chlamydia."

"While Congressman Stockman has a pro-economic growth record, so does Senator Cornyn, as witnessed by his 87 percent lifetime Club for Growth score," the group said, adding that "we do not expect to be involved in the Texas Senate race."

Matt Lewis, a highly regarded conservative writer with The Daily Caller, pronounced Stockman doomed. Conservatives were "in danger of throwing some babies out with the bath water," Lewis said, and he praised the Club for Growth's restraint in Texas as "leadership by example."

It was one of many signs that the tea-party-driven purge of the GOP has begun to subside. Conservative activists still dominate the party and its processes, but their reign of terror may be easing. Consider:

Rep. Paul Ryan, a darling of the Republican conservative base and a likely 2016 presidential candidate, just reached a budget agreement with Democrats that would allow a modest increase in spending. Even the hint of a spending increase was enough to produce howls from Heritage Action this week before the deal was announced. The group, influential among activists and GOP lawmakers, issued a statement Monday that it "cannot support a budget deal that would increase spending in the near-term for promises of woefully inadequate long-term reductions."

The agreement is nothing for either side to celebrate: Raising revenue through fees and gimmicks, it does nothing about the problems with entitlement programs, it doesn't reform the tax code and it doesn't even fully replace the automatic "sequestration" spending cuts. But what's noteworthy is that the threats from conservatives didn't deter Ryan.

At the same time, Senate Republicans are stepping up their efforts to help each other beat back primary challenges. The National Republican Senatorial Committee is going to battle against the Club for Growth and other conservative groups over a primary challenge to veteran Sen. Thad Cochran of Mississippi. Roll Call reported that Senate Minority Leader Mitch McConnell, who has a primary challenger in Kentucky backed by some of the same groups, is holding a fundraiser this week for Cochran. (Historically, the committee has saved its money for general-election battles.)

Concern is also spreading on the right that House Speaker John Boehner of Ohio is planning to defy the tea-party set on immigration reform. Reports in conservative media outlets say that the speaker is planning to hold off on immigration votes until after primary filing deadlines have passed. That way, lawmakers needn't fear a challenge from somebody criticizing a vote for "amnesty." A Boehner spokesman called the reports rumor, but some GOP lawmakers are hoping the speaker pursues just such a strategy.

Stockman, the would-be senator, must have thought he had gamed the system just right when he entered the primary battle against Cornyn on the last possible day. He seems to have calculated that his extreme views would automatically make him a contender, but it hasn't turned out that way.

Nobody can out-conservative Stockman. The former street vagrant, on his second tour in Congress, has been known for inviting Ted Nugent to the State of the Union speech, for opposing Boehner's re-election as House speaker (because of "betrayal of conservative principle") and for his bumper sticker announcing, "If babies had guns they wouldn't be aborted." He launched his campaign Monday by criticizing the "liberal" Cornyn because the incumbent didn't wholly support Texas Sen. Ted Cruz's brinkmanship over Obamacare.

But Cornyn, a former Texas attorney general, is no liberal; he notes with pride that National Journal ranked him the second-most conservative senator last year. The difference between incumbent and challenger is character: Cornyn has it, Stockman is one. That the Club for Growth can recognize the difference is reason for hope.

Follow Dana Milbank on Twitter, @Milbank.