WASHINGTON — After Democrats delivered a resounding counterpunch to President Trump at the polls, one of his most reliable voting blocs — social conservatives — now faces the repercussions of its uncompromising support for Mr. Trump’s agenda.

That result is mixed: Social conservatives are celebrating a slightly expanded Republican majority in the Senate, which advances their top priority, confirming conservative judges, as well as their anti-abortion rights agenda. But steep Republican losses in the House, particularly in suburban areas, have some strategists reflecting on how to proceed as they pivot their efforts to re-electing Mr. Trump in 2020.

“Social conservatives need to maximize turnout from the base and expand the map by stressing the softer side of the faith agenda: education reform, immigration and criminal justice reform, and anti-poverty measures,” said Ralph Reed, founder of the Faith and Freedom Coalition, which has extensive outreach to conservative evangelicals in battlegrounds across the country.

“This will help with suburban women, millennials and minorities,” he said.

That approach, if followed, would be a stark departure from the issues social conservatives have championed since they wed themselves to Mr. Trump as a candidate. The Republicans’ white, religiously conservative base has motivated its troops for Mr. Trump around opposition to abortion rights, a conservative majority on the Supreme Court and support for Israel.