In interviews, other allies of the president who were instrumental in the Kavanaugh fight said that the impeachment inquiry was a much different and, in some ways, more difficult case for them to defend in the court of public opinion because of its complexity.

Much of Mr. Trump’s public response, and the defense from his surrogates, has focused on the process of impeachment rather than the actual facts of the case. But it is harder to rally public support around questions of due process and fairness than it is to simply insist that the president has committed no wrongdoing.

Part of what was so simple about the Kavanaugh case was that conservatives believed him over his accuser. But when it comes to the Ukraine episode, polls have shown that the public thinks Mr. Trump has not been truthful about his actions.

And the president has vacillated repeatedly. He has called the House process a “kangaroo court.” Then he vowed to cooperate, insisting he had nothing to hide, only to have the White House announce that neither he nor the executive branch would willingly provide testimony or documents because House Democrats were not following established precedent on impeachment and were denying Mr. Trump due process.

Conservative activists said they sometimes found it difficult to follow the lead of the White House, which has sent mixed signals about how seriously it is taking the prospect that Mr. Trump could be impeached. At a closed-door conference last weekend in New Orleans for the Council for National Policy, a group of conservative movement leaders, Vice President Mike Pence made no mention of impeachment during his speech, which struck some attendees as unusual.

Republicans also had a significant procedural advantage during the Kavanaugh hearings: As the majority in the Senate, they had the sole discretion to set the timetable, which they kept extremely short — to just nine days . But they will not have such an advantage during the first portion of any impeachment proceedings, which House Democrats will dictate.

Ms. Pelosi has vowed to move the investigation along as quickly as possible and would like a vote before the end of the year. But Republicans have been left guessing, along with the rest of the country, about what the investigation might uncover or who else might come forward. This uncertainty has made settling on a messaging strategy more complicated and not as efficient as it might otherwise be.