My HO from another side of the canyon :-)
Though the role of the President in the US is high (as compared with so-called parliamentary republics), but he can't manage the budget any way he likes. Congress is ruling there (isn't it?). In the previous several years there were progressive slow cuttings in the US military budget, now the trend may change the direction, but it would still be a slow growth (even if the President would like to double it). This was the case for many previous decades and nobody cares here in my country.
As for particular Mr. Trump,
AFAIK and what I heard from the media (which I always take with reservations) is that the budget components would be re-balanced. E.g., instead of spending blns for expeditionary forces and expansion of bases abroad, these blns might go for a high-tech new stuff. Is it good or bad for my country - difficult to say (perhaps equally bad). But if I were a taxpayer, this would sound reasonable.