Rep. Raúl Labrador (R-Idaho), a leading Tea Party conservative, pointedly criticized new Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellObama calls on Senate not to fill Ginsburg's vacancy until after election Planned Parenthood: 'The fate of our rights' depends on Ginsburg replacement Progressive group to spend M in ad campaign on Supreme Court vacancy MORE (R-Ky.) on Wednesday, arguing he needed to show leadership and stand up to President Obama on immigration.

“It’s uncanny to me that our leadership … is already sending the message that we’ve already lost this battle,” Labrador said at a gathering of conservative lawmakers on Wednesday.

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“Last year the message was, ‘We cannot get our way because we don’t have a Senate [majority].’ Now this year’s message is, ‘We cannot get our way, because we only have 54 votes.'

"That’s not leadership. That’s not why the American people voted for us."

Labrador’s remarks follow signals from Senate GOP leaders last week they don’t have the 60 votes needed to pass a House-approved bill responding to Obama’s executive actions on immigration.

The House bill would block funding for Obama’s plan to shield millions of undocumented immigrants from deportation, and would also overturn his 2012 executive order that let millions of people brought to the U.S. illegally as children remain in the country.

Senate leaders are now eying a backup plan that would avoid jeopardizing funding for the Homeland Security Department, which expires on Feb. 27.

Labrador took aim at McConnell, who became majority leader earlier this month, but he also said Tea Party favorites in the Senate, Ted Cruz of Texas and Mike Lee of Utah, need to do more to stop Obama.

Otherwise, Labrador said, Senate Republicans should just hand back power to Democratic Leader Harry Reid (Nev.).

“It’s high time that Mitch McConnell stand up and say, 'This is what we are fighting for in the Senate.' That’s definitely what he said during his campaign, so let’s make sure he does it now as the majority leader,” Labrador said at the “Conversations with Conservatives” event, moderated by the Heritage Foundation.

“But it’s also high time that Ted Cruz and Mike Lee and others decide that they are going to start fighting in the Senate, using the Senate procedural rules and not just looking at the House as the place where the fights are going to happen,” Labrador continued. “They also have a responsibility in the Senate to make sure that those bills pass.”

Told about Labrador’s remarks, a McConnell spokesman said the majority leader told reporters last week at the joint House and Senate GOP retreat in Hershey that his plan was to try to pass the House immigration bill.