Is it generally possible to get tickets for baseball spring training games on the day of the game?

Yes. If you can't get any at the box office (doubtful) you should be able to find someone looking to sell extras in the parking lot. Not to worry too much about scalpers-- people like my buddy Tom usually buy for groups of people and have a one or two extras that they'll part with at face value.

I would recommend taking the tickets when you get them. Don't wait and watch, because you never know if the tickets will be available later or not, and what the price would be. So if you know you need to go for sure, why wait. If however you want to wait, and shell out extra money, yes, you will definitely find scalpers selling tickets at the venue, but at what price? You will know at the venue. So carry enough cash. ;)