ATLANTA — Vice President Harris told a boisterous Atlanta arena on Tuesday that the next 98 days would be a fight, but they’d win come November, as she taunted President Trump for wavering on whether he’d show up for their upcoming debate.

“The momentum in this race is shifting,” the likely nominee said. “And there are signs Donald Trump is feeling it.”

Little more than a week ago, Georgia appeared to be slipping out of the Democrats’ reach: President Biden’s campaign pledged to concentrate more on holding the Midwestern “blue wall” states and indicated they might be willing to forsake “Sun Belt” battlegrounds.

Now that Mr. Biden has bowed out of the race, though, and Ms. Harris is the likely nominee, Democrats are expressing new hopes of an expanded electoral map.

In the state that delivered Mr. Biden his narrowest victory margin in 2020, Ms. Harris pulled off what has been a signature Trump event: A big, loud rally full of supporters cheering her name, as she mocked her rival and his running mate Senator Vance as “just plain weird,” and derided their policies as backward, outdated, and dangerous.

Trump earlier said he’d debate Ms. Harris, but is now questioning the value of a meetup and saying he “probably” will debate her, but he “can also make a case for not doing it.”

Ms. Harris seized on it. “So he won’t debate me, but he and his running mate have a lot to say about me,” she said. “And by the way, don’t you find some of their stuff to just be plain weird.”

“Well Donald,” she said, addressing him head-on. “I do hope you’ll reconsider. Meet me on the debate stage … because as the saying goes, if you’ve got something to say, say it to my face.”

Trump has suggested the September 10 debate on ABC News should be moved to a different network, calling ABC “fake news.”

Ms. Harris hasn’t yet formally seized the Democrat nomination, though she is the only person who met the qualifications to vie for it, the Democratic National Committee announced Tuesday, and will all-but-certainly clinch it come Monday when the party concludes a virtual roll call vote.

Her pick of a running mate is also expected by early next week, when Harris plans to begin a seven-stop tour of battleground states to hold rallies alongside her vice presidential nominee.

On Tuesday, the roughly 8,000-capacity basketball arena at Georgia State University was filled to its rafters with voters waving signs, dancing to the Harris campaign soundtrack and a performance by Megan Thee Stallion.

Such an atmosphere would not have been possible just 10 days ago, with the party reeling over whether the 81-year-old Mr. Biden would remain in the race after a dismal performance magnified concerns about his age and abilities and ultimately ended his campaign.