The reason I don't think a veto-on-principle would have been very effective is that this omnibus spending bill is basically a national budget, and members of Congress will defend voting for it on that basis. It's hard to justify throwing the whole thing out on the basis of a few wrinkles, and that's exactly the tactic they're using to push this through.

Now whether Trump's objections will do anything is another question - I'm not sure they even need to vote on them individually (as people on TD are saying) or if they can just sweep them aside as a whole. But I do think that an outright veto would have done nothing.