(CNN) -- Republicans in the House of Representatives expressed outrage with one of their compatriots on the other side of the Capitol Wednesday, questioning whether or not Texas Sen. Ted Cruz is really all-in on defunding Obamacare or if he's trying to put all the onus of defunding the bill on the House.
The House outrage stems directly from a statement from Cruz and fellow GOP stalwarts against Obamacare in the Senate, Marco Rubio and Mike Lee. In it, Cruz said Senate Republicans simply don't have the votes necessary to keep defunding language in the continuing resolution to fund the government after Oct. 1. Republicans have been attempting to push a bill that would fund the rest of the government while defunding the health care law, a bill Democrats have vowed to fight.
"(Senate Majority Leader) 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 the statement.
"At that point, House Republicans must stand firm, hold their ground, and continue to listen to the American people. President Obama has already granted Obamacare exemptions to big corporations and Members of Congress; he should not threaten to shut down the government just to deny those same exemptions to hard-working American families."
The idea that Republicans don't have the votes to defund Obamacare is not new from Cruz. He's spent the summer trying to build a "tsunami" of grass-roots outrage against the Affordable Care Act, arguing that such a movement would be the only way to kill President Barack Obama's signature legislation.
The reaction from House Republicans and senior GOP leadership aides to Cruz's latest statement on the matter was swift and angry, both about Cruz's lack of confidence in a vote and his urging of the House to "stand firm."
"They said nothing is impossible if you fight hard enough, and the minute the House announces the vote, they give up the fight? It's crazy," one senior GOP leadership aide told CNN.
"They should walk the walk," the aide said, predicting it would backfire on the conservative senators.
Another senior GOP leadership aide took a shot at Cruz declining to say whether he would filibuster the bill, telling CNN, "It is disappointing to see that Wendy Davis has more balls than Ted Cruz," in reference to the state senate Democrat who filibustered an abortion bill in the Texas legislature over the summer.
Cruz's Texas GOP colleague, Rep. Blake Farenthold, said he hasn't seen the statement but heard a lot of grumbling from House Republicans on the chamber floor about it Wednesday night.
"We gave them what they asked for; I was more hopeful they would be more positive about it and fight for it," Farenthold said.
Farenthold praised Cruz as one of the most articulate legislators on the Hill and issued a challenge: "I think this a great opportunity for him to go to the Senate floor and win over some votes. Let's see him do the Rand Paul filibuster. He can do it, and I think he'll do a good job," Farenthold said.
The Texas delegation has a regular lunch on Thursdays, and Farenthold said he hopes Cruz shows up tomorrow so they can discuss strategy.
Arkansas Republican Rep. Tim Griffin took to Twitter to tweak Cruz, Rubio and Lee, referring to a message from a reporter about the their statement and tweeting "so far Sen Rs are good at getting Facebook likes, and townhalls, not much else. Do something. . . RT ..."
A spokesman for House Speaker John Boehner was more muted in his response. "We trust that Republicans in the Senate would put up a fight worthy of the challenge Obamacare poses," Michael Steel said.
Cruz aide Sean Rushton stood up for his boss when asked for comment on the GOP ire. A filibuster of Obamacare still hasn't been ruled out, Rushton said. "All options are on the table," he said.
In a statement, Rushton continued, "The ball is in Harry Reid's court. Reid has the votes ONLY IF Republicans don't stand strong. Sen. Cruz will continue working to win the argument with both his colleagues and the American people."
CNN's Dana Bash and Ted Barrett contributed to this report.
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