SANTA FE, N.M. — It is legislative season in New Mexico, which means it is time once again to debate whether illegal immigrants should be granted driver’s licenses.

For the third straight session, Gov. Susana Martinez, a Republican, will be pushing to repeal a nearly decade-old law that allows New Mexico residents who are in this country illegally to obtain the licenses.

Debate over the issue has not only bitterly divided lawmakers in the state — one of only two that permits illegal immigrants to get the same licenses as citizens — it has also become a recurring theme of Ms. Martinez’s tenure.

This year’s legislative session, which convened Tuesday, promises to be no different as both sides gear up for another contentious battle over the issue.