At this scale, we're dealing with the curved Earth, and that makes this a somewhat tricky problem.
I'm assuming your points are all west of the Prime Meridian, and that you're looking for distances to states at constant 90 degree bearings (i.e., traveling eastward, always along a latitude parallel).
For each point, you could get it's lat/long, and make a new corresponding point at that latitude, and at zero longitude (the Prime Meridian). Make that point with an attribute field that the original points contain too, and see that corresponding point pairs have the same, unique attribute value.
Make lines (rays) between the point pairs, using your line id field (http://help.arcgis.com/EN/ARCGISDESKTOP/10.0/HELP/index.html#//00170000003s000000).
Convert your states to line features (http://help.arcgis.com/EN/ARCGISDESKTOP/10.0/HELP/index.html#//00170000003t000000).
In a geographic coordinate system (e.g., WGS84) where parallels are all straight and west-east, calculate the intersection points of each line with the state lines.
Use field calculations to get the lat/long of your starting points and intersection points, along with their unique ids from your lines, into the attribute tables. See that intersection points also carry their state name attribute. Export these to csv.
The shortest distance from your start points and the intersections is not along that constantly-90-degree line, it's along the Great Circle arc between the pair of points. Use a tool like this one (http://gis.harvard.edu/tools/software/great-circle-distance-batch-calculator) to calculate the distances. You'll have multiple intersection points (two or more) per line; the one at shortest distance for that line is your closest one, and the state it belongs to is your closest state to the east.