WASHINGTON (CNN) — Arizona Sen. John McCain said Wednesday he believes there is still a chance for the immigration bill, currently stalled in the Senate, to come forward for a vote.

“I am guardedly optimistic – and I emphasize guardedly – optimistic that we can get the bill to the floor of the Senate just before the fourth of July recess, and pass it through the United States Senate," McCain said while campaigning in Los Angeles.

The GOP presidential hopeful said he has been in daily consultation with his colleagues in the Senate, as well as the White House, in hopes of moving the bill forward.

Senate Majority Leader Harry Reid pulled the controversial bill from the Senate floor last Thursday after a motion to stop debate on the measure failed. Though several Republicans wanted to add amendments, Reid said debate had lasted too long.

On Tuesday, Reid said it's up to Republicans to collect more votes in favor of the measure to convince him that reviving debate could lead to passage.

McCain also took a shot at potential presidential rival Hillary Clinton for including earmarks, or narrowly targeted spending requests, in the Defense Authorization bill currently before Congress.

He said the New York Democrat had over one hundred million dollars in such funds attached to the bill, and added, “We can’t do this earmarking and pork barreling if we’re ever going to be careful and serious stewards of the taxpayers dollars.”

A vocal critic of earmarks, or pork barrel spending as it is also known, McCain said he would work to eliminate the practice as president.

– CNN's Jamie Crawford