The gun-rights lobby dramatically showcased its strength this week by helping boot two state senators from office in the first-ever recall election in Colorado, a crucial state in the national debate over gun control.

The recall, which claimed the jobs of Senate President John Morse, from Colorado Springs, and Sen. Angela Giron, from Pueblo, was supported by the National Rifle Association. It targeted the two Democratic senators for their support for new laws that subjected private gun sales to background checks and banned...