If D.C. voters split their vote between Republicans and Democrats, we would have a better chance of achieving representation (the taxation part we already have), because Republicans in Congress would be slightly more likely to enfranchise the city if they didn't think that do so would mean the creation a reverse-Utah on the Potomac. But this is a real tilting-at-windmills exercise. Most of the people I know around here would sooner give up their Volvos than vote Republican, even for tactical reasons in meaningless races.
This article available online at:
http://www.theatlantic.com/politics/archive/2010/11/life-in-a-single-party-state/65563/