Ms. Gilligan said the foundation has an endowment and doesn’t expect its grant programs to be significantly affected in 2018, but there is concern about the longer-term impact of the tax change. “Eliminating the tax incentive,” she said, “has the potential to have a very negative impact on charitable giving.”

United Way Worldwide, ranked the largest charity in 2017 by donations by Forbes, is recommending that its community-based affiliates contact important contributors to highlight the changes that are coming, said Steve Taylor, the charity’s vice president of public policy. United Way Worldwide provides leadership and support to its network of groups across the country. “We’ve been urging them to reach out to big donors and talk to them about tax reform,” he said. Typically, the local United Way chief executive or head fund-raiser has a personal relationship with important donors, he said, and will talk by phone. (“My donors,” said Mr. Kimbrough of the United Way of Greater St. Louis, “have my cellphone.”)

Some 26,000 to 28,000 major donors nationally give a total of about $500 million a year to United Way, in gifts of $10,000 or more, Mr. Taylor said. Some of those donors may be affected by the change in the standard deduction. Donors give for altruistic reasons as well as tax breaks, Mr. Taylor said, but the increase in the standard deduction is expected to have an impact.

“They’ll still give,” Mr. Taylor said. “But they’re going to give less.”

(Millions of smaller donors, who make pledges to the United Way through workplace contribution programs, average gifts of $150 a year. They have already made their elections for next year’s donations.)

Major donors are often concerned about stability, Mr. Kimbrough said. So they may structure gifts to donate more this year and receive a larger deduction, but space out the funds for spending over several years to help smooth out any budget gaps.

Elie Hassenfeld, co-founder and executive director of GiveWell, a nonprofit organization that recommends a handful of charities, said nonprofits are in a “zone of uncertainty.” But the group has frequent one-on-one conversations with its donors, he said, and is raising the issue of tax reform with them. The message? “You should be thinking about the possibility that your desire to deduct is going change from this year into the future,” he said.

Eileen Heisman, chief executive of the National Philanthropic Trust, which oversees donor-advised funds, said the trust is seeing some larger gifts this season. “People would rather gift when they know what their tax benefit is going to be,” she said.