I do not know very much about museums specifically. What I do
know about is the dynamics of the budgetary process. Anyone else can
also know what I know (or at least most of it) by reading and digesting
the writings of the legendary Aaron Wildavsky.
Speaking of legendary, the National Park Park Service attained
that status once upon a time by its perfection of the
"Washington Monument" gambit. In each budget cycle its people
would solemnly testify in the reauthorization hearings that,
unless it got its request (base+increment) it would be forced -
would have no choice, no alternative - to shut down the
Washington Monument. Its people knew full well that right down
there at the other end of the Mall were the House and Senate
office buildings where every Honorable's constituents, visiting
the Nation's Capitol from Podunk and outraged at finding their
vacation spoiled, could express their opinion if not to the
very Honorable him/herself, at least as close as an outer
office.
By their heroic and well-intentioned efforts the Washington museums
have made a very big mistake. They have blown the only
strategic advantage or leverage they had. What- do they expect
to benefit from some sort residual "good will?" Remembered warm
and fuzzies on the part of the patrons? Get real.

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