“Thus incited by President Trump, members of the crowd he had addressed…unlawfully breached and vandalized the Capitol, injured and killed law enforcement personnel, menaced Members of Congress, the Vice President, and Congressional personnel, and engaged in other violent, deadly, destructive, and seditious acts,” the impeachment resolution, which won support from 10 Republicans, alleges.

The Senate could take the next steps—trying Mr. Trump and voting on his guilt—as soon as this week. Conviction requires a two-thirds vote by senators present; assuming perfect attendance, 17 Republicans would need to join all 50 Democrats to find Mr. Trump guilty.

Many Republicans are gravitating toward a technical argument: The Senate lacks jurisdiction to try him after he leaves office, they maintain, because he will be a private citizen. That could allow the Republicans to thread a political needle, voting against Mr. Trump’s conviction without having to defend his conduct, people familiar with the discussions say.