After the House GOP leadership on Wednesday agreed to push a defunding Obamacare measure to the Senate as part of the continuing resolution, the shutdown squadron of Republican Sens. Ted Cruz (Tex.), Mike Lee (Utah) and Marco Rubio (Fla.) put out a statement praising the House.

Sen. Ted Cruz (R-Tex.) (Gary Cameron/Reuters) Sen. Ted Cruz (R-Tex.) (Gary Cameron/Reuters)

But then, in a move that sent some House members into orbit, the senators conceded the measure lacked the votes in the Senate and would go nowhere: “Harry Reid will no doubt try to strip the defund language from the continuing resolution, and right now he likely has the votes to do so,” Cruz said in a statement. “At that point, House Republicans must stand firm, hold their ground, and continue to listen to the American people.”

A number of House Republicans were infuriated. Many were skeptical all along about how a shutdown strategy would work. Here Cruz and company had been grandstanding — only to tell them the whole thing was a lark and then demand the House stand firm. “Our members are really pissed at his comment,” one senior House aide fumed. “If he simply acknowledges they didn’t have the votes, he proves our point.”

The outrage is genuine, but it is also an opportunity for House Republicans tired of the holier-than-thou crowd in the Senate ginning up the base to pressure House members to push back. The attitude now seems to be: If this thing flops we’ll make certain our voters know it was Cruz et al who took us down a blind alley.

The National Review Online, often complimentary of Cruz, found the same outpouring of outrage from House offices, commenting that “it’s fair to say Cruz’s statement was tone-deaf, and he has not articulated a sophisticated strategy for getting Reid and Obama to buckle and repeal the president’s signature legislative achievement.” That is precisely what critics of the suicidal shutdown team have been saying for weeks.

Some of the anger in the House no doubt reflects annoyance building over time that Cruz and hecklers like Heritage Action have become obsessed with attacking Republicans instead of Democrats. (NRO points out that Cruz was at it again on talk radio, quoting him as saying, ” Right now, I can tell you, the people who are fighting the hardest against our efforts to defund Obamacare are not Democrats, it’s Republicans. It’s Republicans who have been leading the onslaught, trying to stop this. Because they’re afraid of the political risk. They’re afraid of being blamed politically.”) One House aide dismayed at the intra-party fights told me, “I just think our political energy and attention should be focused on weakening the Left.”

Another GOP aide caustically observed, “Him surrendering to Harry Reid on the CR before the House even put it up for a vote proves he’s just a hairdo.” Yet another adviser e-mailed Right Turn: “The House has effectively led the fight against Obamacare for three years, with results. It’s easy to be in the Senate minority and make grand claims. We want a House and Senate majority that gives us real leverage, which is made more difficult if Cruz and Lee keep the fight focused on Republicans.”

The incident may be a blessing in disguise for the House, which is now forewarned that they proceed at their own risk. As one GOP aide put it, “It’s time for Cruz and Lee to really show us what they have in the Senate. That press release gave the impression that the answer is ‘not much’.”