Republican House leaders reiterated their opposition Sunday to the immigration bill passed by the Senate last week, highlighting the uncertain prospects for enacting a major overhaul of the nation’s immigration laws.

“The Senate bill is not going to pass in the House,” House Judiciary Committee Chairman Bob Goodlatte, R-Va., said on CNN’s “State of the Union,” echoing statements made by House Speaker John Boehner, R-Ohio, and other senior Republican lawmakers.

Even Sen. John McCain, R-Ariz., a leading supporter of the Senate legislation, acknowledged the difficult path the bill faces in the Republican-controlled House.

“I’m concerned about the task ahead,” he said on “Fox News Sunday.” “It’s not going to be easy.”

Boehner has said that he will not bring up an immigration bill for a vote that does not have the support of the majority of the Republican House caucus.

Goolatte noted Sunday that the vast majority of Senate Republicans voted against the Senate bill, which would create a system to confer legal status on 11 million immigrants in the country illegally while bolstering border security and tightening employment rules through an electronic system to verify workers’ immigration status known as e-verify.

But many conservative lawmakers say the security provisions of the Senate bill are inadequate and may never be implemented.

“There is a diminution of trust among our fellow citizens,” Rep. Trey Gowdy, R-S.C., who chairs the House Judiciary Committee’s immigration subcommittee, said on Fox News. “And the notion that I can tell them, ‘We are going to provide legalization, but trust us on the border security, trust on the internal security, trust on e-verify,’ that’s not going to fly in South Carolina.”