As many here know, I'm a believer in small government.
That being said, I think the main purpose of government is to keep people safe, and the NWS does exactly that.
Now, I'm not saying that I totally disagree with the President here. Like every other government agency, I'm sure there is quite a bit of wasteful spending and some corruption within the NWS.
I remember a few years ago when talk of privatization came up and nearly everybody cried foul. As long as it's done right, private management of the NWS is not a bad idea. It would have to be government subsidized so potentially lifesaving weather information will remain free to the general public.
Bring in company A to manage the NWS. If they do a bad job, fire them and bring in company B to see if they can run it more efficiently. If not, bring on company C.
REMEMBER: GOVERNMENT IS A MONOPOLY.
They have no competition, and as a result, there really isn't any incentive to do a good job.
I know there are many dedicated government employees, but we've all encountered some who obviously don't give a crap.