Gov. Charlie Baker says he’ll “certainly veto” a bill that would let illegal immigrants in Massachusetts get driver’s licenses — a proposal critics say would make the Bay State a magnet for fraud.

“I would certainly veto legislation that gets beyond what we actually worked with the Legislature on a bipartisan basis to put in place,” Baker said Thursday. “I mean, the law that we signed basically said if you have lawful presence in Massachusetts you can get a driver’s license for the period in time of which you have lawful presence. I think that’s the right answer.”

The policy stance came a day after state Sen. Brendan P. Crighton (D-Lynn) and Reps. Tricia Farley-Bouvier (D-Pittsfield) and Christine Barber (D-Somerville) introduced the Work and Family Mobility Act, which would strip the portion of the current law that says people illegally in the country cannot get Massachusetts licenses.

When told of the governor’s position, Crighton told the Herald, “I hope he would let it go through the process and take a look at the merits of the bill.”

The legislators behind the bill said it would make the roads safer because people would be held to the same standards, having to pass tests and get insurance. They also said the state has the moral responsibility not to overburden the 210,000 illegal immigrants estimated to live in Massachusetts.

“There is no pathway to citizenship for them because of failures at the federal level,” Crighton said. “We have to recognize that they are here, and they’re parts of our community and the economy.”

Some Massachusetts legislators have tried to get policies like this passed over the past few years, but without much success. Baker introduced an amendment to stop illegal immigrants from getting licenses in 2016, when the state passed the Real ID law.

The Massachusetts Chiefs of Police Association said it’s still weighing what position to take on the current bill and declined further comment until that decision is made.

Twelves other states, including Vermont, Connecticut and California, allow illegal immigrants to get driver’s licenses.

But Jessica Vaughan of the anti-illegal-immigration Center for Immigration studies said people in the country illegally will flock to the Bay State with false papers in an attempt to get legitimate ones.

“It opens up the opportunity for fraud — it may end up with non-citizens getting on the voter rolls,” Vaughan said. “It sends the signal that there’s nothing wrong with being here illegally. We should not be endorsing this.”