“I promise no voter in New York is saying, ‘I wish more campaign ads were on the air,’” said Glen Caplin, an adviser to Ms. Gillibrand, adding that the campaign was continuously evaluating the state of the race. Her campaign has taped a television ad in case it is needed.

“We’re trying to do it a little differently,” Ms. Gillibrand explained. “What that looks like is I’ve done 16 town halls; I’ve been to all 62 counties; I’m trying to really create a grass-roots-oriented campaign and a modern campaign.”

Some of Ms. Gillibrand’s limited spending has been geared to an audience far beyond New York.

In recent weeks, she has bought Facebook ads nationally to raise money for Democratic senators and Senate candidates, including Kyrsten Sinema in Arizona, Claire McCaskill in Missouri and Jacky Rosen in Nevada. (Donations are split between Ms. Gillibrand’s campaign and the candidates, while her campaign harvests valuable new donor contacts.)

She is running other ad programs to expand her database of supporters: In late September, a series of Facebook ads, which also ran nationally, featured a one-question survey: “Do you approve of President Trump?” Pathmatics said she spent $183,000 on one such ad.

A study by academics of Facebook ad data compiled by Pathmatics showed that Ms. Gillibrand spent $1.5 million on Facebook ads through August, but only 9 percent of it in New York. In contrast, 82 percent of spending on Facebook ads by Senator Amy Klobuchar, a Minnesota Democrat who is also up for re-election, was within her state.

Senator Bernie Sanders, who is also on the ballot this year, spent only 1 percent for ads in his home state, Vermont, the study showed. The heavily favored Mr. Sanders has also spent little on his re-election, ending September with $8.8 million in his campaign account, though he is not expected to face the same financial pressures as other candidates if he runs again for president, because he already has an expansive donor base. His 2016 campaign was powered by more than $230 million in mostly small contributions.

Ms. Gillibrand, Ms. Warren and Mr. Sanders would all enjoy one other financial advantage if they run right after getting re-elected: Not only can they transfer everything left over from their Senate campaign to a presidential committee, they can also tap again every past donor, even those who have given the legal maximum of $5,400 in the 2018 cycle, because it would be a new campaign.