A bipartisan group of senators today reached an agreement on immigration overhaul, and the bill’s first test will not be long in coming: a key procedural vote will be held May 21.

The bill, the product of months of negotiations among Republicans, Democrats and the White House, could still encounter considerable opposition.

The legislation would allow the estimated 12 million illegal immigrants now in the country to stay and work, but they would have to wait up to eight years to apply for green cards.

They would have to return home before being eligible, and pay a fine of $5,000.

A new temporary worker program would allow new immigrants to come and work for up to six years, but they would have to return home every two years.

A key goal for Republicans has been ending so-called “chain migration” of family members of new arrivals by incorporating a new point system for awarding green cards that would include other factors.

A Democratic aide said that under the deal more than 50 percent of green cards still would go to spouses and non-adult children of immigrants. Only about 30 percent of the new green cards would be subject to a new merit-based system, which would award points based on job skills, education and English proficiency.