“A large reason he was chosen was to help Romney govern,” an adviser to the campaign said. “Paul’s going to focus on being a partner.”

Democrats in the Bush years, of course, criticized Mr. Cheney for usurping for himself a kind of co-presidency.

Mr. Ryan and Mr. Romney seem to have an effective partnership on the trail; the younger man has been deferential to a fault since he was tapped for the ticket, modifying long-held positions to conform with Mr. Romney’s. That said, Mr. Ryan has made clear that he would not be relegated only to attending funerals.

Before Mr. Ryan accepted the nomination, aides said, he had extensive conversations about his position with Mr. Romney, who assured him he would play a guiding role on fiscal and economic matters. Already seen as an intellectual leader of the Republican Party because of his sweeping House budget proposals, Mr. Ryan would wield the clout that comes from being recognized as the party’s most likely next in line for the presidency, prominent Republicans said.

“My guess is Paul will be an extraordinarily consequential vice president,” said Representative Tom Cole of Oklahoma, a member of the Republican House leadership, who was a visitor to the Ryan family box during the Republican convention in August. “He’s going to play an important role in outlining, shaping and passing the Romney agenda from the day he walks in the door.”