SANTA FE, N.M. (AP) — The New Mexico Legislature sued Republican Gov. Susana Martinez on Friday over budget vetoes that would effectively eliminate the legislative branch of government by cutting off its funding amid an escalating clash over how to resolve the state's financial crisis.

The move by the Democratic-controlled Legislature was an extraordinary step in a drawn-out feud over budget shortfalls that already have triggered cuts to public school athletic programs, layoffs at state museums and shortages of public defenders. Without a compromise, New Mexico runs the risk of closing down it...