Passing new restrictions on voting — in particular, tougher limits on early voting and vote-by-mail — is now at the heart of the right’s strategy to keep donors and voters engaged as Mr. Trump fades from public view and leaves a void in the Republican Party that no other figure or issue has filled. In recent weeks, many of the most prominent and well-organized groups that power the G.O.P.’s vast voter turnout efforts have directed their resources toward a campaign to restrict when and how people can vote, with a focus on the emergency policies that states enacted last year to make casting a ballot during a pandemic easier. The groups believe it could be their best shot at regaining a purchase on power in Washington.

Their efforts are intensifying over the objections of some Republicans who say the strategy is cynical and shortsighted, arguing that it further commits their party to legitimizing a lie. It also sends a message, they say, that Republicans think they lost mostly because the other side cheated, which prevents them from grappling honestly with what went wrong and why they might lose again.

Some also argue that setting new restrictions on voting could undercut the party just as it was making important gains with Black and Latino voters, who are more likely to be impeded by such laws.