Maybe they could just fire Calista Flockhart. She's probably the highest paid actor on the show (even though she's just a B-list actress, they seemed to make a big deal out of her being on the show). Heck, fire Flockhart and the actress that plays Lucy Lane, move the show to Vancover and the CW network, and they'd save money and probably get a quality increase.
I don't know that I'd be interested in a Cat Grant-less Supergirl; the relationship between Cat and Kara is pretty key to the show.
That said, one of the primary concerns I had with Supergirl is that the show could have benefited from focusing on either CatCo or the DEO rather than juggle both. If the series had to ditch one work environment or the other for budgetary reasons, I'd recommend ditching the DEO. That doesn't mean getting rid of Alex and J'onn, it just means moving them into a different place. (Maybe Alex goes to work for Maxwell Lord.)