Republican senators criticized border security provisions in a new immigration bill Tuesday, arguing that the landmark legislation can’t pass Congress unless the measures are strengthened.

“If in fact the American people can’t trust that the border is controlled, you’re not going to be able to pass this bill,” said Sen. Tom Coburn of Oklahoma, top Republican on the Senate Homeland Security and Governmental Affairs Committee. “You’re going to have to do a lot more on border control.”

Sens. Rand Paul, R-Ky., and Ron Johnson, R-Wis., voiced similar concerns at a committee hearing to examine border security provisions of the bill, which is to face its first votes on Thursday before a different panel, the Judiciary Committee. Amendments are expected to be offered during the Judiciary session to boost the border provisions of the bill, which was introduced last month by four Democratic and four Republican senators.

One of the legislation’s authors, Sen. Marco Rubio, R-Fla., has already acknowledged that the bill will face a tough road to passage if the border security elements are not improved.

Paul, a tea party favorite who’s voiced support for a comprehensive immigration overhaul, insisted his goal in raising questions about the bill is to make it better so it can pass not just the Democratic-controlled Senate but also the Republican-run House. He denied that he’s out to oppose the bill or slow it down.

“I want to be constructive in making the bill strong enough that conservatives ... will vote for it,” Paul said.

“If it’s not any stronger than this I don’t see it getting through the House,” he said.

Echoing concerns raised by a number of Republicans, Paul said that the bill relies too much on setting goals and requiring studies about border security, instead of insisting on actual accomplishments. Under the bill, “You have to have a plan to build a fence, but you don’t have to build a fence,” he complained.

The bill allocates $5.5 billion for border measures aimed at achieving 100 percent surveillance of the entire border and blocking 90 percent of border crossers and would-be crossers in high-entrance areas.