A controversial proposal to make undocumented immigrants eligible for New York driver’s licenses has skidded onto the statehouse front burner after Democrats captured control of the state Senate this month. Advocates for the measure contend it would enhance public safety in New York by allowing people who are in violation of immigration laws and are already driving to properly register and insure their cars and trucks. The legislation would allow license applicants to use passports issued by another country as a form of identification accepted by Department of Motor Vehicles officials. Persons who lack a Social Security number would not be denied a license if they certified they had never received one, under one bill filed in both the Assembly and the Senate.