These programs that have not really been major powers, Wisconsin, Colorado, or have pretty much fallen out of that level, like Nebraska, all think they can get there but I’m not sure they ever will. Nebraska and Miami are sort of the poster children for programs that lost there way when they left for new leagues. The Huskers recruited the southwest, especially Texas, for skill players. In the Big 10, that connection was lost. Kids from Texas went to Nebraska knowing they’d play 2-4 games in front of the home folks each year.
Nebraska didn't play many games in Texas until they joined the Big 12 in 1996. They were in the Big 8 conference which was Oklahoma, Kansas, Iowa St., Colorado, Missouri, Kansas St., Oklahoma St. They have played over 85 games against Iowa St., Oklahoma, Kansas St., Missouri, and Kansas. They have played 62 games against Minnesota and 52 against Iowa. The most games they have played against teams from Texas are 14 against both Texas and Texas A&M, most coming when they were in the Big 12.
As for recruiting, I checked the 1994 national championship roster. Six were from Texas and none were offensive skill players and one was a DB. The vast majority of the roster was from Nebraska (especially walk-ons), and 12 were from California, and 5 each from Florida, New Jersey, and Missouri.
I think the structural problem that Nebraska has faced is that when they were on a roll (primarily before they joined the Big 12), they were always on TV because they were one of the top teams and there weren't many games shown on TV. Nebraska recruited nationally due to name recognition and accomplishments. Now, Nebraska does not hold the same cache with recruits or college football fans in general. I think they can be a perennial top 25 team, but I don't think they can win a national championship anymore.