It's too late to ask pretty much any girl to any prom, anywhere in the United States. For a girl to buy a prom dress is generally not something that happens overnight. Proms are also wicked expensive - is he footing the bill for this nonsense? Seriously, we are talking a few hundred, maybe even a few thou (no exaggeration), between limo, attire, flowers, dinner, prom tickets, and any after party activities.
If your father wants you to socialize, forcing you into the highest pressure situation of the year is just plain stupid.
You are not helping things. Asking one girl and then just not bothering with anyone else is not really trying that hard. I recognize that you aren't into most of the girls at your school, but if that's the case, then rejection or asking wouldn't be that fraught with emotion or shyness, right? And saying that you would rather sleep or play video games doesn't help, either (even if it's true). If he's seeing you growing fat and lazy (or thinks you are, or is afraid you will), then he's concerned. Maybe overly so, but he's concerned.
Is he perhaps concerned about your sexuality? I'm being serious here. Is he pushing you to do this because he thinks you may be gay? Because if that is his motivation, it's a lousy way to go about it, and your going (or not going) wouldn't prove it one way or the other, anyway.