In an appearance on CBS' "Face the Nation," Ayotte said the bill's provision allowing a pathway to citizenship for the 11 million undocumented immigrants living in the United States was "a tough but fair way for them to earn citizenship."
"I've looked at this very carefully," she said. "This is a thoughtful bipartisan solution to a tough problem."
The likely Democratic and Independent votes of support for the legislation should add up to 54, CBS News said.
Joining Ayotte to make up the remaining necessary votes are the four Republican members of the so-called "gang of eight" senators who wrote the legislation -- John McCain and Jeff Flake of Arizona, Lindsey Graham of South Carolina and Marco Rubio of Florida.
Likely providing the sixth Republican vote is Sen. Orrin Hatch, R-Utah, who made a deal to pass the bill through the Judiciary Committee last week, but hasn't committed to voting it into law, CBS News reported.
Rubio warned the legislation still has an uphill battle because a floor debate, scheduled to begin Tuesday, must result in increased border security provisions to win support from conservatives in both the Senate and House.