There are millions - millions! - of old bikes in the world with this tire size. It's still an active, new factory bike tire size in Japan, and a very common wheelchair tire size worldwide. Despite this, some folks claim you can't find tires this size.

Here's the 26x1 3/8 aka EA3 aka 650A tires I found available on the 'net, at my LBS, at suburban big boxes and small town hardware stores about a year ago, including some knobbish ones for the OPs 'cyclocross' type use.

Bell Sports Streetster (folding)
Chengshin C638
Continental City Ride
Hutchinson Junior
Innova Cloud Nine
IRC Super Gold
IRC City POPS
Kenda gumwall
Kenda Cross (knobby)
Kenda K40 Street
Michelin World Tour
Nutrak Traditional
Nu-teck (airless)
Panaracer Col de Vie
Panaracer Passhunter (light knobby)
Panaracer ST Daily Commuting
Pyramid gumwall
Pyramid Sunlite Hybrid Nimbus
Raleigh Record (NOS)
Rubena Flash V66
Schwalbe Delta Cruiser (available in cream color)
Schwalbe Marathon
Schwalbe Marathon Plus
Schwalbe Speedway Pro (knobby)
Specialized TriSport
Vittoria Randonneur
Vredestein Perfect Tour
Vredestein Dynamic Tour
Vredestein Classic