A “Texas mile” is similar to a “country mile”—it’s a long distance. Texas is big, so a “Texas mile” would be something longer than your average mile.
 
 
(Dictionary of American Regional English)
country mile n
an indefinitely long distance.
1951 TN Folk Lore Soc. Bulletin 17.58 wTN, Long as a country mile.
     
1 March 1952, Helena (MT) Independent Record, pg. 8, col. 2:
Their nearest rivals are seven strokes behind, a Texas mile so to speak, and Bolt admits that “it looks like it’s between Jack and me.”
   
2 February 1953, Oakland (CA) Tribune, pg. D25, col. 1:
Spalding, incidentally, first was attracted to young Jimmy by his ability to demonstrate to the customer world that Spalding balls could be belted a Texas mile with Spalding clubs.
 
15 February 1957, Hammond (IN) Times, pg. 8, col. 5 ad:
“This whiskey’s best by a Texas mile. Sunny Brook whiskey, that is!” 
 
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Maverick Gold
by Dean W. Ballenger
Manor Books
1977
Pg. 47:
...that rawhidin’ bastid came and Bass, who was a Texas mile from being a gunslinger, had the only defending guns.
     
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Counterfeit Cowgirl
by Heather Allison
Harlequin Books
1994
Pg. 20:
A Texas mile was obviously much longer than a New York mile.
 
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Taste Pure and Simple:
Irresistible Recipes for Good Food and Good Health
by Michel Nischan with Mary Goodbody
San Francisco: Chronicle Books
2003
Pg. 94:
I would never serve leg of lamb with mint jelly—in fact I would never have a jar of it within a Texas mile of my kitchen!