But that source might run dry if President Trump gets his way. His full budget proposal, expected to be released on Tuesday, will zero out the program, which funds efforts like Meals on Wheels, homeless shelters for veterans, and in Ms. Rodriguez’s case, water improvements for her rural community, which voted for Mr. Trump.

Mr. Trump, who wants to build a wall on the border with Mexico and increase defense spending, has said that the grant program is “not well targeted to the poorest populations and has not demonstrated results.”

Robert Rector, a senior research fellow at the conservative Heritage Foundation who specializes in welfare and poverty, called the program a “model of inefficiency.”