WASHINGTON — Vice President-elect Mike Pence stood beneath the nine chandeliers of the Trump International Hotel’s Presidential Ballroom, a modest walk from the soon-to-be Trump residence, with a dinnertime soundtrack of well-heeled donors clinking glasses and looking forward to an incoming administration of their conservative dreams.

“We are just 44 days away from when Donald Trump will be inaugurated as the 45th president of the United States of America,” Mr. Pence said, to building cheers, at a gathering on Tuesday night hosted by the right-leaning Heritage Foundation. “We did it.”

Mr. Trump’s upset victory last month — along with his often shape-shifting policy proposals during and after the campaign — has left many groups eager to brand the triumph as their own, racing to frame the outcome as an argument for desired legislative aims.

And if Mr. Trump’s early personnel decisions in the transition are instructive, to say nothing of his choice for vice president, perhaps no group has more to celebrate than the conservatives in this room, who hope that a champion as unlikely as a Manhattan reality television star can preside over a whirring machine of unified Republican government.