“I think it is a time when we remember the presidency itself, the whole institution of the presidency as something that binds us,” she said. “These moments allow you to feel the history of the country and the belonging. We belong to George Washington and Abraham Lincoln and the forefathers, that is part of who we are. This president is part of that family line.”

Like Reagan and Ford, the presidents before them and those still to come, Mr. Bush took steps as president that infuriated some Americans, ended badly and cost lives and money. But he also served with dignity and distinction in the military and various public posts, tried to stir Americans to greater civic involvement and enacted economic policies that paid off while posing a distinct threat to his own political fortunes.

“Whether people agree with every policy that President Bush undertook, you always knew that he did what he thought was in the country’s interest even when it was politically disadvantageous to him, such as the budget agreement with the Democrats,” said Senator Susan Collins, Republican of Maine, referring to the 1990 agreement that broke his “no new taxes” pledge. “Right or wrong on the policy, that was a very brave action to take, and it probably cost him the election.”

“My hope is that as we take this pause to honor this great man, that we think about how he governed, the respect and dignity that he showed to adversaries and to friends alike,” said Ms. Collins, who paid a final visit to Mr. Bush at his home in Kennebunkport, Me., in September. “George Bush represented an era where you could disagree with someone but still respect and even like the person, where a search for a common ground was applauded, not denigrated.”

She is hardly alone in hoping that the focus on Mr. Bush’s humanity and willingness to compromise spurs some introspection in Washington in a time of intense and volatile political warfare. Senator Amy Klobuchar of Minnesota, who as the senior Democrat on the Rules Committee is involved with coordinating memorial events, said the funeral could be Mr. Bush’s “final gift” to government as a remembrance of the virtues of compromise when Congress is trying to resolve multiple year-end legislative conflicts after a contentious midterm election.

“He makes everyone step back and remember why we are really here,” said Ms. Klobuchar, who added that events such as the funeral enable “us to step back as a country and remember those who have done extraordinary things like George H.W. Bush. If we don’t do things like this, we have lost our sense of democracy.”

But recent experience does not give much occasion for optimism that any sense of unity and common ground will be long lasting.