“When somebody who understands the Senate and loves it as much as he does says it’s time to make a change to accomplish a paramount result that the nation needs, it does have an effect,” Mr. Kaine said.

For some presidents, choosing to support a change in Senate rules to protect voting rights might also have foreshadowed a broader awakening to the realization that the Senate was no longer a place where partisanship could be put aside for the good of the country.

That is certainly the view of many in his party, who assert that far-reaching legislation like the president’s Build Back Better package and gun control proposals are doomed to falter without wholesale changes to the Senate’s rules.

In effect, they argue that today’s intense partisanship has led to an ideological stalemate that justifies burning down the house in the name of progress on many fronts.