* Ayotte's backing may draw other Republicans
* Fellow Republican Senator Paul hedges on support
* Legislation faces tough battle in House
Republican Senator Kelly Ayotte on Sunday threw her support behind a sweeping U.S. immigration bill, calling it a "thoughtful" reform that would ease the burden of illegal immigration and allow companies to more easily hire qualified workers.
Support from Ayotte, who has been courted by the bill's backers, could pave the way for other Republicans to endorse the measure in the Senate, where a vote is expected by the end of June.
"Our immigration system is completely broken," Ayotte, of New Hampshire, told CBS' "Face the Nation" program. "This is a thoughtful, bipartisan solution to a tough problem, and so that is why I am going to support it."
Ayotte, an ally of Senator John McCain of Arizona, one of the bipartisan "Gang of Eight" senators who crafted the bill, said it would improve border security and ensure the U.S. economy, particularly its high-tech sector, was able to attract the best workers.
She also said the bill deals with the problem of having 11 million undocumented immigrants living in the nation.
The Senate bill is expected to get strong support among Democrats, but will need some Republican votes to meet the 60-vote minimum required for passage.
Many supporters believe the overhaul of immigration laws faces its toughest challenge in the Republican-led House of Representatives, where conservatives have expressed skepticism about the central aspect of the Senate bill, a path to citizenship for undocumented immigrants.
The Senate bill, which is backed by President Barack Obama, also would authorize billions in new spending for enhanced border security and would create new visa programs for high- and low-skilled workers. Obama has made immigration reform a top priority of his second term.
Senator Rand Paul of Kentucky, another Republican whose vote is being sought by immigration supporters, said on Sunday he was open to voting for the bill, but said he would insist on changes, including provisions to toughen border security.
Paul, who has hinted at a possible presidential run in 2016, has backed the concept of a path to citizenship for the undocumented, but criticized the bill for not having a mechanism to assure that the U.S. border with Mexico is secure. He also wants visa programs that allow companies to hire foreign workers expanded.
"I am the conduit between conservatives in the House who don't want a lot of these things and more moderate people in the Senate who do want these things. I want to make the bill work, but see, the thing is, what they have in the Senate has zero chance of passing in the House," Paul told the "Fox News Sunday" program.
"I'm really trying to make immigration work, but they are going to have to come to me and they're going to have to work to make the bill stronger if they want me to vote for it," Paul added.
Both Republican and Democratic senators are likely to offer amendments to the bill to bolster border security, considered by critics to be a weak link in broad immigration reform.
Skeptics of comprehensive reform warn of the risk of a repeat of 1986 when President Ronald Reagan signed legislation that offered amnesty to 3 million undocumented immigrants, but failed to obtain the level of border security that backers had anticipated.
These critics complain that the 1986 amnesty ended up attracting more illegal immigrants.
Democrats have vowed to fight any amendments - including those on border security - that would create too many obstacles to the 13-year path to citizenship included in the Senate bill.
The "Gang of Eight" senators are trying to preserve Democratic priorities in the legislation while courting enough Republican votes to ensure its passage.