WASHINGTON — In recent days, lawmakers were told that when President Trump ramped up his campaign to pressure Ukraine into helping him against his domestic political rivals, he directed advisers to his personal lawyer. “Talk with Rudy,” he instructed. But one thing lawmakers will not do is talk with Rudy.

Rudolph W. Giuliani was hardly the only offstage character during two weeks of impeachment hearings that ended on Thursday. Lawmakers also heard that Mike Pence and Mike Pompeo were in the loop, that Mick Mulvaney organized the political equivalent of a “drug deal” and that John R. Bolton was adamantly against it.

But among those missing from the House Intelligence Committee’s witness list, besides Mr. Giuliani, were Mr. Pence, Mr. Pompeo, Mr. Mulvaney and Mr. Bolton. Not that the panel’s Democratic majority was necessarily uninterested in talking with the vice president, secretary of state, acting White House chief of staff or former national security adviser. Democratic leaders have decided not to wage a drawn-out fight to force them to testify over White House objections.

Instead, as the committee wrapped up its public hearings on Thursday, House Democrats have opted for expeditious over comprehensive, electing to complete their investigation even without filling in major gaps in the story. It is a calculated gamble that they have enough evidence to impeach Mr. Trump on a party-line vote in the House and would risk losing momentum if they took the time to wage a court fight to compel reluctant witnesses to come forward.