Gov. Charlie Baker's veto of a union-backed collective bargaining dues bill was easily overturned Wednesday in the House, as all but one Republican lawmaker deserted the governor and joined Democrats in backing the so-called Janus bill.

Baker's override did not trigger any debate in the House and could be completed when the Senate meets on Thursday afternoon.

Labor Committee Co-chairman Rep. Paul Brodeur of Melrose said the bill's passage would bring an end to "free riders" who he said are able to access union services in grievance situations without being a member or paying dues to cover such services.

Rep. Shawn Dooley of Norfolk was the only Republican House member to vote to sustain Baker's veto, which the governor said stemmed from employee privacy concerns raised by the bill.