Our military needs their money to create and sustain critical jobs here and buy billions worth of military tools most of which they barely know how to use.
The US relies on Saudi oil.
Saudi Arabia relies on US protection.
Each benefit mutually from petrodollar pricing -- the US guards against devaluing its currency (and reducing the value of dollar-denominated assets within its financial system), Saudi Arabia, and virtually every oil-exporting nation, benefits by not having their currencies appreciate in the absence of any meaningful domestic demand for foreign goods.
There are other elements, though those are the large ones.
Actually the US does not need Saudi oil. Yes, we do import from them, but we can easily replace them. We get almost 4x as much oil from Canada as we do from Saudi Arabia, by the way.
So, while the US may not burn Saudi oil directly, it is absolutely dependent economically on Saudi Arabia supplying a critical share of global oil.
More significantly, as the global surplus producer, Saudi Arabia took over the role the US had played from 1930 - 1971 in setting and establishing global oil prices. The result hasn't been quite so, ahem, well-oiled as the TRO's production quota and certificates of clearance (US Dept. of Interior), but it's been the one handle on extraction volumes, and hence, price, that's been available.
The other thing is that while the US isn't necessarily dependent on Saudi oil, key allies and trading partners are. Places like Japan, China, EU states, etc. That gives them a lot of strategic leverage.
https://www.washingtonpost.com/news/worldviews/wp/2016/04/05...
Also they are largely running their own war in Yemen against the Houthis. And it the Saudis that are flying those sorties.
http://www.independent.co.uk/news/uk/politics/uk-has-sold-56...
You're thinking of Israel.