What's the least number of straight lines across America do you need to intersect every state?

You need just one.
Just place some black holes at the appropriate positions.
They will warp spacetime, so from an outside reference frame, the line will have curves, but from the reference frame of the line itself, it will be completely straight.
Alternatively, if you mean ‘on a world map’ just angle the line ever so slightly, and when it loops around it will intersect every state, and depending on the angle, even every point on the map.

A straight line has no curvature. If the slope of the line must be constant, then you’d need to start looking at secant lines since earth is an ellipsoid. It would be less than 25 lines, though. This is because you can (and should) have the secant line intersect at two or more borders, such as the four corners.

Bridges of Königsburgönigsberg

Graph theory

Combinatorics

Chinese Postman Problem aka Traveling Salesman Problem

we are not assuming it’s on a globe sorry should have said.