Continued from page 1

Mr. Rubio has been vocal about changing the legislation in order to win the 60 votes needed to clear the Senate without a filibuster. In fact, he has signaled that he might not vote for the bill as it stands.

Speaking on ABC’s “This Week” program Sunday, Mr. Rubio was asked whether he would vote for it and called it “an excellent starting point.”

“I think 95, 96 percent of the bill is in perfect shape and ready to go. But there are elements that need to be improved. This is how the legislative process is supposed to work,” he said.

So far, that legislative process has been slow.

The Senate officially turned to the bill Tuesday, and lawmakers began to file amendments. As of Thursday, when the Senate wrapped up business and went home for the week, 107 amendments had been submitted. Just one, by Sen. Chuck Grassley, Iowa Republican, received a floor vote.

Mr. Grassley wanted to restructure the bill so that the borders are secure before any illegal immigrants are legalized. As written, the bill gives illegal immigrants almost immediate status, though a full pathway to citizenship is years in the future.

Senators rejected Mr. Grassley’s amendment on a 57-43 vote. That signaled the core of the immigration deal struck by Mr. Rubio and his seven fellow bill authors is intact, though it is not attracting tremendous support within the Republican Party.

Among the more than 400 pages of other amendments are proposals to build hundreds of miles of double-tier fencing on the border, to limit the number of guest workers allowed into the country, to promote English as the official language, to have illegal immigrants admit they are in the U.S. in violation of the law, and to make businesses certify that they aren’t replacing Americans with foreign workers.

One major fight looming is another border security amendment from Sen. John Cornyn, Texas Republican. The 134-page measure would allow illegal immigrants to get legal status, but would delay their chance at citizenship until strict border security metrics are met.

As written, the bill requires the government to spend billions of dollars but doesn’t tie legalization to results on the border. The bill does tie legalization to certain interior enforcement measures.

Top Democrats have called Mr. Cornyn’s amendment a “poison pill” that would scuttle the bill, but Mr. Rubio and fellow Republican authors of the bill reject that notion and say they would like to find a way to incorporate some of Mr. Cornyn’s ideas.