A bipartisan group of eight senators four Republicans and four Democrats drafted the bill and then guided it to approval in the Senate Judiciary Committee, where Sen. Orrin Hatch joined the two Republican authors in supporting the bill. However, Hatch says he will vote for the measure again only with changes.
Separately, Sen. Marco Rubio, R-Fla., said he will vote for the bill he helped write only with changes.
As drafted, the legislation also creates a low-skilled guest-worker program, expands the number of visas available for high-tech workers and de-emphasizes family ties in the system for legal immigration that has been in place for decades.
The legislation creates a 13-year route to citizenship for an estimated 11 million immigrants currently living in the United States illegally.
The bill is a "tough but fair way" for the estimated 11 million to come "out of the shadows" and "earn citizenship go to the back of the line, pay taxes, pass a criminal background check, learn English," Ayotte told CBS' "Face the Nation."
It also sets border security goals that the government must meet before immigrants living in the U.S. illegally are granted any change in legal status.
"As a nation of immigrants, we must remember that we're all descended from people who came here from somewhere else in search of a better life," she said.
"But the broken immigration system we have now is unworthy of a great nation," she added. "It's time for Washington to tackle this problem head on."
Despite support from the White House, the AFL-CIO labor unions and the pro-business Chamber of Commerce, the bill's passage is by no means assured. Sixty votes are usually required to end Senate debate and consider adoption. There are currently 54 senators, including two independents, in the Democratic caucus, and 45 Republicans.
Leaders in the Democratic-led Senate want a final vote on the legislation by July 4.
The Republican-led House, meanwhile, is taking a smaller, piecemeal approach to the issue.
Immigration also has deep political implications.
In 2012, President Barack Obama won re-election with the backing of 71 percent of Hispanic voters and 73 percent of Asian voters. A thwarted immigration overhaul could send those voting blocs more solidly to Democrats' side in future elections. That has led some Republican lawmakers to support immigration reform, but the party's conservative base still opposes any legislation that would create a pathway to citizenship for immigrants living here illegally.
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