Georgia. Ohio. Texas. Democrats Tell Biden to Go Big (He’s Being Cautious).

Senator Sherrod Brown of Ohio is pushing the former vice president’s aides to commit resources to his state, a longstanding political battleground that, after Mrs. Clinton’s dismal showing, many Democrats had concluded was out of their grasp.

“Ohio was a bellwether until 2016,” Mr. Brown said, arguing that Ohioans, unlike Sun Belt voters who’ve backed only Republicans, can be lured back because they’ve long voted for Democrats like Mr. Biden.

Mr. Biden’s advisers point out that he needs only 270 electoral votes to win and that remains their first objective. Their caution reflects the sobering possibility that, in the end, none of the conservative-leaning states will flip to Mr. Biden, and that his lead in Florida and the critical Midwestern states is more tenuous than polls suggest right now.

“When you look under the hood, we are ahead in the majority of the battleground states, but we expect them to tighten because these are battleground states in a pretty polarized electorate,” said Ms. O’Malley Dillon.

While Mr. Biden’s aides assess the landscape, Mr. Trump is signaling where he thinks the race is headed.

Last week, the president spent just over $150,000 on television ads in Michigan, where polls have him significantly trailing, while he poured over $1.3 million into commercials in Georgia and over $600,000 in Ohio, where surveys show a dead heat, according to the firm Advertising Analytics.

No state offers as big a temptation, and potential payoff, as Texas, with its increasingly Democratic, and diverse, urban centers. Beyond its importance in the presidential race, Texas provides House Democrats more pickup opportunities than any other state and the prospect of claiming a majority of seats in the state House and on the state Supreme Court, both of which could prove pivotal for redistricting.