The driver's certificate would allow someone without a Social Security number to get a permit to drive and buy insurance.
Nebraska Motor Vehicle Department Licensing Administrator Sara O'Rourke said that if the bill passes, illegal immigrants wouldn't have to worry about being turned in to immigration officials.
A 2004 study found that nationwide, the at-fault driver in injury accident was without insurance in about one in seven cases. The study said Nebraska's rate of uninsured drivers was 7 percent.
A Nebraska Office of Highway safety official said the department believes the number is much higher than that today.