DENVER — A populist backlash against Colorado’s new gun-control laws claimed its third political casualty on Wednesday as a Democratic state senator resigned her seat rather than face a recall vote that could have cost her party control of the chamber.

For Democrats in this swing state, the resignation of the senator, Evie Hudak, was a sign of the growing political cost of their votes last winter to expand background checks and limit the size of ammunition magazines — measures once hailed as breakthrough victories in the effort to respond to mass shootings.

Polls show that voters embrace aspects of the new laws. But the measures have infuriated gun advocates and Republicans, and have become political liabilities in a state where the gun debate is shaped by traditions of hunting and sport-shooting, as well as by the shadows of mass shootings at Columbine High School and the Century 16 movie theater in Aurora.

In September, two prominent gun-control supporters were ousted in recall elections, reducing the Democrats’ edge in the State Senate to one seat. Ms. Hudak, who represents the suburbs northwest of Denver, would have been the third to face a recall vote, and she and state Democrats acknowledged that neither she nor the party’s 18-17 majority was likely to survive it.