Question

Why did mexican americans living in new mexico have no representatives in washington,

Answer 1

I believe it's because new mexico was a territory, not a state
Prior to 1912, New Mexico was regarded only as one of the territory that incorporated into united states.
Because of this, hey do not posses any previlege to choose their representative in the Government (which make it impossible for them to influence the election)

Answer 2

Mexican Americans were a minority. They seem to be few in number than their american counterparts, also new mexico is a territory and not a state. Generally In-order to get the focus of the Federal Government to a particular state or territory, the government should own the land with dense population and the land should be home to some naturally found resources and development, where the Federal government did not have to spend a huge money for development. Unfortunately the New Mexico territory doesn't have all these to attract any interests from the Federal Government.