Although appointed, the SCOTUS judges have always represented federal districts (back in the pre-civil war days, they were required to "ride the circuit" and spent much of their tenure visiting local courts in their district. I'd like to return to that system in some form and get these guys to stop being in the beltway year-round).
If we were to switch to an elected SCOTUS, you'd ever have to eliminate two of the federal districts, or expand the membership of the court to 11 Justices (technically there are 13 federal districts, but the Chief Justice represents the DC circuit and the Federal Circuit at large).
I've been intrigued by the idea for a while. One thought that crossed by mind about a decade ago if that my region of the country was "represented" by John Paul Stevens of Chicago, and he could have hypothetically been fired if his district (namely Illinois, Wisconsin, and Indiana) got to vote on whether to retain him in a statewide election.
In any case though, the current map would have to be redrawn to some degree. One of the best things that would come out of a partisan redistricting is that the 9th circuit as we know it would cease to exist. Right now, its obscenely large in both area and population, and would have a hugely disproportionate electorate (compared to the rest of the country) that would make popular elections in the "district" a huge burden: 
Hypothetically, it shouldn't be hard to gerrymander whole states to create a 6-3 or even 7-2 Republican majority on SCOTUS. We'd just pack all the RATs into west coast and northeastern coastal districts. Federal circuits 1 and 2 could be combined into some safe RAT district stretching from Maine to New York.