“Until Democrats win a statewide election, we’re not a purple state,” said Brian Robinson, a Republican political consultant in Georgia. “We may be a purpling state. But until they win, this is a red state.”

It is just such a historic rout of Mr. Trump that some Democrats increasingly believe is necessary to send a political message to Republicans, a moral one to the rest of the world, and serve a key logistical purpose: getting a clear Electoral College winner on Nov. 3, rather than waiting for an extended ballot counting process.

To many, a commanding victory that sweeps Democrats to control of the Senate as well would set the stage for a consequential presidency, not just one that evicts Mr. Trump.

“What they’re going to need in order to move the country forward is to demonstrate that a ton of people are with him and are aligned with his agenda,” said María Teresa Kumar, chief executive officer at Voto Latino, a voter mobilization group that has endorsed Mr. Biden. “That the people want to address climate change in a big bold way. They want to address health care in a big bold way. And they want to address education in a big bold way.”