[...] the President may propose to Congress that funds be rescinded. If both the Senate and the House of Representatives have not approved a rescission proposal (by passing legislation) within 45 days of continuous session, any funds being withheld must be made available for obligation. Congress is not required to vote on such a proposal and has ignored most Presidential requests. [...] The Act was passed in response to Congressional feelings that President Nixon was abusing his ability to impound the funding of programs he opposed, and effectively removed the historical Presidential power of impoundment.

I think you are correct: the president can make changes, but cannot deliberately "starve" programs he doesn't like.

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sapere aude