While I can understand being upset about one day, he's being unreasonable: most people don't take three days off for their own birthday, let alone their partner's. And frankly he shouldn't be putting you in this spot in the first place.
Lay it out for him: you love him, but you can't take three days off from a job you just got, or you won't have a job. Point out that your time unemployed was pretty rough for you and that you both really need the money. Then work out a compromise; doing something fun with him that he really wants to do...on your day off.
He's got to understand that you may love him, but life doesn't always work out that he comes first.
Let's get real, three days off work for your boyfriends birthday is not reasonable. There will be other events that will arise when time off will be a legit request and maybe with just a bit of perspective and maturity he might know the difference.
I think I would be pissed off at his immaturity. I'm wondering what kind of employee he is. What a brat.