By Caren Bohan
WASHINGTON, June 25 (Reuters) - Republican Senator Marco Rubio, shifting his tone on the U.S. immigration bill he helped to write, said on Tuesday he is now fully satisfied that the measure will do what it takes to secure the southern border with Mexico.
Rubio, a potential presidential contender and the most high-profile Republican backer of immigration reform, had irked supporters of the sweeping Senate immigration bill with public comments in which he consistently said the legislation was not tough enough on border enforcement.
The Florida lawmaker was part of the bipartisan "Gang of Eight" senators that in April unveiled the bill that would provide a path to citizenship for millions of undocumented immigrants while beefing up border security and creating new guest worker programs for high- and low-skilled workers.
The Senate measure appears headed for passage this week, with supporters expecting a strong showing of around 70 votes in favor of it. An amendment on border security crafted by a small group of Republicans has helped to persuade several in the party to give their backing to the bill.
At a cost of $46 billion, the amendment would double the number of agents on the southern border to about 40,000 and provide more high-tech surveillance equipment.
"This amendment basically now puts into place virtually everything people have been asking me to do about immigration enforcement since I began talking about this issue," Rubio told a convention of the American Society of News Editors. "I think we've run out of things we can to do to support - to improve the border."
In a series of television and radio interviews over the past two months, Rubio had said he did not think the bill could get a sufficient number of Republican votes needed for passage without stronger border language and that his own vote depended on such changes.
Alex Conant, a spokesman for Rubio, said that while the senator is now satisfied with the border language in the bill, he would still like to see votes on some other changes, including an amendment under discussion that would further bolster the system employers use to verify workers' legal status.
Passage of the immigration bill in the Democratic-led Senate would send the measure to the Republican-dominated House of Representatives where it faces a much tougher sell. Many conservatives have denounced the plans to give legal status to the undocumented as "amnesty."
Asked about House Speaker John Boehner's strategy for handling the immigration issue in that chamber, Rubio said it is up to House lawmakers to determine the course they want to take.
But he added: "I think we have a good piece of legislation they should take a look at. There are a lot of good ideas that they should adopt."
Speaking with reporters on Capitol Hill, Senator Lindsey Graham, another Republican member of the Gang of Eight, urged the House to "give us their version" of an immigration bill so that the two chambers can work on a compromise.
"If they don't agree with the bill, that's fine, but not having a solution on the table I think is unacceptable for the Republican-controlled House," the South Carolina senator said.
At the news editors event, Rubio, who is often mentioned as a potential 2016 presidential contender, was asked if he was considering a run.
"I know that you're not going to believe me when I tell you this. I really don't think about that right now," he said, adding that his decision would depend on many factors including what would be best for his family and whether he wants to run for another term in the Senate. (Additional reporting by Rachelle Younglai; Editing by Mohammad Zargham)