That's the budget sent to Congress, and traditionally pronounced "dead on arrival". In practice, the Congress is usually pretty interested in continuing to fund existing programs (many of them mandated by law), and changes (adding and removing stuff) is done around the edges.
The final appropriations bill (authorization to spend money) is passed by the House, then the Senate, and then possibly reconciled between the two.
That's then sent to the President, who can sign it or veto it. The veto could be overridden, but it's a very high bar to clear, and the President's party nearly always has enough votes to avoid that even if they're not an outright majority. So then there's a protracted negotiation... during which the government may shut down if the existing appropriations bill expires (including temporary extensions).
[0] With minor exceptions, ie they have to originate in the House because that is the body with the power of the purse.
Congress can only override his veto with a 2/3rds majority, that is highly implausible.
If congress and the president can't come to terms on a budget, our government effectively shuts down [1] in what is, largely, a form of political gamesmanship.
[1] https://en.wikipedia.org/wiki/Government_shutdowns_in_the_Un...
Strictly speaking, if congress doesn't pass a budget the previous year's budget is in effect for some things, and others can be handled at the level of a 'continuing resolution' that doesn't require the president's signature.
Realistically all parties (house/senate/exec) generally come up with a deal, which is sometimes a proper set of spending bills, and sometimes a hack-up of short term fixes.
He also generally has a lot of unofficial influence with legislators in his party, so he can use that influence to push things one way or another. That's usually the main effect, and Trump would likely just use his influence on the senate here.
The Senate is controlled by his party, and Mconnell has shown time and again he won't stand up to the president (he won't agree with him either, but will use it politically for his own agenda). So I don't expect a budget Trump objects to will even make it to his desk.
What is likely to happen is that the Senate will use this as a negotiation tool with the house. It -will- lead to a compromise eventually (but with a decent chance of government shutdown first), which will end up funding most of the things Trump wants, AND most of the stuff Dems want, leading to a further increase in the deficit.