Is work one's way across an idiom or does it mean literally?
I should like to travel and work my way across the USA.
I am planning to work my way across Australia.
I work my way across every program.
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I want to work my way across the USA
has two potential meanings, depending on context.
I want to travel from one side of the USA to the other while working at various jobs along the way to pay for the trip.
It is similar to the meaning of "I worked my way through college."
The other meaning is
I want to travel across the USA without a fixed plan, probably slowly and possibly remaining at various places for a more or less prolonged stay.
It is similar to the meaning of "They worked their way through the unexplored jungle."
To be sure of which meaning is intended, you need additional context.
Your "across every program" is not idiomatic in the U.S. What would be far more likely to be said is "through every program."