There are good political reason why DC will never, and should never, become a state. Considering that the US is supposed to be a collection of states, giving DC statehood would give one state an unfair amount of power over the other states. Not only do they get representation (which they would rightly deserve, if they were to become a state), but they would also house the federal government. The whole point of DC NOT being a state, as I understand it, was to avoid giving any one state more power than any other. Whether or not housing the government would actually reflect additional power is irrelevant; the possibility or even the perception of a possibility of damaging the republic by granting a state more power than it deserves (based on the design of the constitution) is sufficient to deny it.
If a vote were to occur, you’d have a hard time getting states onboard to vote for it. Large states will be upset that the citizens of DC will be so unfairly represented in the sentate. Smaller states will be upset that a lower population gets equal representation in both houses (with the exception of Wyoming, which apparently has a smaller population than DC). Of course, you’ll also get resistence from the red states. No state has anything to gain from voting for an ammendment to allow DC to become a state, so I’d have a hard time imagining more than a handful of votes for it, muchless the requisite 37.
Someone correct me if I’m wrong, but its my understanding that the original intention of DC was not to house citizens; it was intended to house government officials, foreign nationals/diplomats, etc. Thus, there was no need for representation, as the officials there have a vote in their native state, and the foreigners have no voting rights. That this is not true today is a failing of management, not of design.