The effort is spearheaded by Wisconsin tea party groups and pro-life activists, who feel betrayed by Mr. Ryan's nearly $2 trillion package.

The spending bill avoided a government shutdown by surrendering on conservatives' top priorities, including giving up the fights to defund Planned Parenthood and to block President Obama's plan to bring at least 10,000 Syrian refugees to the U.S.

The hunt is on to find a suitable conservative candidate who can beat Mr. Ryan, who received 94 percent of the vote in the 2014 primary in his district, which sits against the Illinois border in the southeastern part of the state.