Sen. Marco Rubio (R-Fla.), in an interview Tuesday with Fox News Channel, said the immigration reform compromise he is helping lead doesn't have the 60 votes it needs to pass.

"No, and I think even the Democrats would concede that," Rubio said. "And there's a few reasons for it, but one of the things we've learned over the last few weeks ... is how little confidence people have that the federal government will enforce the law."

Rubio added that people are only going to be on board if "we can make sure that this never, ever happens again" -- specifically that a new influx of illegal immigrants wouldn't result from passage of the bill.

"This is nowhere near being done," Rubio said. "I'm optimistic that something good for our country can happen, but it needs to happen the right way."

Another key member of the so-called Gang of Eight that crafted the bill, Sen. Charles Schumer (D-N.Y.) predicted Sunday that the bill would pass by the July 4 recess.

The bill passed easily out of the Senate Judiciary Committee by a vote of 13-5. Three Republicans voted for it.