The National Endowment for the Humanities does great work. <a href="https://www.neh.gov/our-work" rel="nofollow">https://www.neh.gov/our-work</a>. Why should the White House want to close it down.
It's important to remember that in negotiations, both sides strategically establish their initial demands to be much more extreme than what they ultimately expect to receive. That is the case here. The Executive branch is posturing for budgetary negotiations. The NEH will likely survive, perhaps with a diminished budget, as a concession.