The total end strength of the National Guard, from all fifty states, is approximately 350,000.
National Guard are one weekend a month and two weeks per summer. Divide the end strength by 26 to get an idea of how many bodies would be available for patrolling the borders at any one time, unless you permanently federalize the Guard and keep them on active duty forever.
So, with approximately 13,500 bodies available, we want to man the posts 24/7. To man a single post in three shifts requires five people (the other two are spares to allow for illness, support requirements, et cetera). Therefore, you have 2,700 personnel on post at any one time.
These personnel must secure 6,000 miles of border (4,000 or so along the Canadian border, and the balance forming the US-Mexican border).
This works out to one soldier patrolling about 2.25 miles of border, or a two-man patrol covering 4.5 miles.
That's not even a "thin screen." That's anorexic.