As long as Senate Republicans stick with Mr. Trump as expected, the House Democrats prosecuting the case will not be able to muster the two-thirds vote required for conviction. Just as important to the president, though, is framing the debate in a way that he can take onto the campaign trail as he battles Democrats for a second term.

This team may not provide the sort of defense the president’s most combative supporters feel he needs. Stephen K. Bannon, the president’s former chief strategist who has been hosting a daily radio show and podcast on impeachment with a group that often coordinates with the White House, said the addition of Mr. Dershowitz and Mr. Starr brought impressive legal power to Mr. Trump’s team.

But Mr. Bannon expressed concern that “there are no fire breathers,” as he put it. “It’s very conventional in its makeup and approach. But this is not playing on C-Span. The senators are not the jury; the American people are the jury. I strongly believe you need some of the fire breathers from the House, like Matt Gaetz, Jim Jordan, Mark Meadows and Lee Zeldin.”

Mr. Trump wanted some of those congressmen, among his most stalwart House Republican allies, to be on the defense team, but Senator Mitch McConnell, Republican of Kentucky and the majority leader, rejected the idea. Those House members, who are familiar with the testimony provided by witnesses during the impeachment inquiry, are expected to help behind the scenes and to help defend the president on television, people familiar with the president’s legal defense plan said.

Mr. Trump’s team is also preparing for the possibility that witnesses will be called in the trial, despite Mr. McConnell’s hope to avoid it.

Other lawyers joining Mr. Trump’s trial team include Pam Bondi, the former Florida attorney general who has been a spokeswoman for the defense effort; Jane Serene Raskin, who defended Mr. Trump during the investigation by the special counsel Robert S. Mueller III; and Eric D. Herschmann, a partner at the law firm of another of Mr. Trump’s longtime lawyers, Marc E. Kasowitz.

The president has wanted media-savvy defenders who could play the same vocal role that his personal lawyer Rudolph W. Giuliani did during the Mueller investigation. Mr. Dershowitz has been a media figure for years and Mr. Starr was a contributor to Fox News until parting ways with the network because of his new role with Mr. Trump.