A motion to pass House Bill 158 failed on 27-38 vote.
But the House, on a voice vote, later agreed to reconsider and place the bill on the calendar, meaning it can be taken up again at some point.
Supporters argued it would help law enforcement officers and could lead to a decrease in auto theft rates.
Opponents said they heard repeatedly from constituents who said they like the current system, especially the ability to put decorative plates on the front.
Earlier Saturday, in a committee meeting, State Police Chief Pete Kassetas testified some criminals intentionally park stolen cars in such a way to conceal the back-end license plates.
“This would just give another layer of protection to officers who are identifying vehicles,” Kassetas said during Saturday’s hearing.
New Mexico is currently one of 19 states that only require license plates to be affixed to the rear-end of vehicles.
The proposed legislation, sponsored by Rep. Patricio Ruiloba, D-Albuquerque, would have changed that.
However, the bill has been met with public resistance, as several lawmakers said they have received a flood of emails in opposition to the proposal.
There are nearly 2.3 million registered New Mexico license plates, according to a fiscal analysis of the bill, and the legislation would have imposed a new $2 vehicle registration fee intended to offset the cost of making and issuing more plates. It would have applied to both new registrations and license renewals.
Skeptics of the legislation questioned whether such a law is needed in rural New Mexico and said it could impose a cost on consumers.
“Honestly, I don’t like the front license plate brackets anyway,” quipped Rep. Eliseo Alcon, D-Milan, during the committee hearing.