I expect him to have a good (maybe even great) series against Miami. They have no shotblocking and Chalmers/Hobbled Wade aren't better perimeter defenders than Conley/Allen. George Hill, a much less skilled PG than Parker, is averaging 14 points on 48 percent shooting in the series. Also worth noting is Parker won't have to expend much energy on the defensive end guarding Chalmers. He should excel.
Spurs don't match up too badly with the Heat, but the reason they're a big underdog is because they don't have Lebron (and if Wade returns to form, then it's lights out). Simple as that.