Not exactly - she is the DC "delegate" to the House of Representatives. Since D.C. has no representation in Congress she merely observes the proceedings and can attempt to influence the 435 real representatives to vote for things she may want. Essentially she is a lobbyist paid for by taxpayers.

There have been several attempts to essentially make DC behave like a state (they do get 3 electoral votes in presidential elections) but for now it is not and Norton is powerless. Personally, I would like to see DC be considered part of Maryland for Federal voting and representation rather than be literally a city-state but that's just me. For now it is what it is and she does not carry the weight you suggest. (For my 2 cents of politics, I'm grateful she doesn't!)