The original Senators stuck it out from 1901 through 1960. (Washington: first in war, first in peace, last in the American League.) That team moved to Minnesota, where there was a long tradition of high-grade minor league baseball to sustain it. A pennant in 1965 also helped get the team off to a good start with local fans.
The expansion Senators started up in 1961 and lasted through the 1971 season. That team moved to Arlington, Texas, smack in the middle of the hugely populated Dallas-Fort Worth metropolitan area. The size of the fan base helped to sustain the Rangers until the team finally got into post-season play in 1996.
Now the failed Montreal Expos seem to be headed to D.C. The transplanted Expos will spend a few years in old D.C. Stadium, due east of the Capitol building (but far from the gentrified precincts of Capitol Hill). The team will then move to a new park on the Anacostia River in southeast D.C.
To succeed financially, the new Washington team must draw well from the Maryland and Virginia suburbs. Attendance will be high for a few years, because the closeness of major-league baseball will be a novelty to fans who've had to trek to Baltimore to see the increasingly hapless Orioles. But suburbanites' allegiance to the new Washington team won't survive more than a few losing seasons -- and more than a few seem likely, given the Expos' track record. As the crowds wane, suburbanites will become increasingly reluctant to journey into the city. And, so, the taxpayers of D.C. (and perhaps the taxpayers of the nation) are likely to be stuck with an expensive memento of false civic pride.
P.S. Baltimore Orioles owner Peter Angelos has to be bought off. He doesn't want a National League team 40 miles from his American League team. Mmmm...remember when Boston, Chicago, New York, Philadelphia, and St. Louis had a team in each league? In fact, New York had two National League teams -- one in Manhattan (the Giants) and one in Brooklyn (the Dodgers). Not only that, but for many years the teams in Philadelphia and St. Louis shared stadiums.