Be sure to scroll down... there may be more than one question on this page!
Paint removal is always difficult regardless of the surface and asphalt is no exception. In fact, one of the "corollaries" of the Murphy's Law of Home Repair is that paint always sticks best and lasts longest on surfaces we didn't intend to paint in the first place. Aside from asphalt, other favorite goofs that come to mind are carpets, rubber weatherstripping, clothing, and wallpaper!
Uncoated asphalt tends to become very porous over time allowing easier staining. Spray paint has a solvent base that tends to bind tenaciously to asphalt… that's why the lines on the roads stay put so long! Any paint solvent or remover will likewise soften the asphalt. Your best recourse is to just coat the driveway (or just the offending area) with a black asphalt sealer available at any hardware or home store. This coal-tar based product will easily mask the paint stain with a more attractive black finish. I would highly recommend sealing the entire driveway. The resulting smooth, nonporous surface makes snow removal easier (I noticed your address) and lengthens the life of the driveway as well. And… future painting "accident" cleanups and… if necessary… touchups will be easier!