The power to appropriate was given to Congress and Congress alone, and quite explicitly can only be done by an act of Congress. Art. 1 Sec. 9. This appears to me to be a constitutionally non-delegable power, especially to a branch of government that it is constitutionally withheld from.
So, to flip the script on the querying, what should Congress do? Refuse to appropriate any money to the executive until he gets back in line? Shut the government down?
Or, worst case scenario, go to court?