Among the star witnesses who could deliver explosive public testimony in front of live television cameras could be John R. Bolton, the president’s former national security adviser, who has been described in testimony as alarmed by what appeared to be pressure on the Ukrainians by Mr. Trump and his allies.

Democrats may also decide to call a string of other diplomats and administration officials, including William B. Taylor Jr., the top American diplomat in Ukraine, who testified in excruciating detail about a quid pro quo in which Mr. Trump and his allies held up security aid and a White House meeting in exchange for an investigation into former Vice President Joseph R. Biden Jr. and his son Hunter Biden.

Privately, White House officials concede they are losing the messaging battle with Democrats, whose inquiry has produced a series of devastating revelations about allegations that the president and his allies conducted a campaign to pressure Ukraine for his own political gain.

People close to Mr. Trump said that the coming weeks will be marked by an increased assault on the integrity of the inquiry itself as the White House tries to avoid litigating the facts of what took place between Ukrainian officials and Mr. Trump’s loyalists, including Rudolph W. Giuliani, his personal lawyer.

White House aides are planning to add communications aides dedicated to impeachment, a move that Jared Kushner, the president’s senior adviser and son-in-law, has pushed for. Among those under consideration to help lead the new team is Tony Sayegh, who recently left the Treasury Department where he was the top spokesman. White House aides have also discussed bringing on in some capacity Pam Bondi, the former attorney general of Florida and a favorite of Mr. Trump’s, a person familiar with the conversations said.

Stephen K. Bannon, who was pushed out as the White House chief strategist in August 2017, has also created an unofficial war room in the basement of his Capitol Hill townhouse to wage over the radio a messaging war on the Democratic impeachment effort.

Mr. Graham said that Mick Mulvaney, Mr. Trump’s acting chief of staff, has assured him that the White House is “working on getting a messaging team together” and said he hoped it would be as effective as the one that Bill Clinton’s White House assembled during Mr. Clinton’s impeachment in the late 1990s.