If I remember my history correctly, there were rumblings in Congress about looking into revoking MLB's anti-trust exemption when the first Senators left, and that got everybody in gear to put a new team in DC, pronto.
You probably already know this, but the other AL team in that expansion move was the Los Angeles (sic - they were originally the LA Angels before becoming the California Angels, and now they're back to how they started) Angels, who played their first few seasons in Chavez Ravine, aka Dodger Stadium. Seems that the AL was feeling left behind in the wake of the westward move of the game (the KC Athletics were the league's westernmost team at the time) and wanted to make amends as quicly as possible.