I'd probably call VT a "near-helmet", much like Wisconsin, Oregon, Texas A&M, etc. They don't have the instant-recognition of Notre Dame (even most non-football fans associate the Irish with college football) but for those who pay at least some attention to CFB, they know they're at least somewhere in the Top 25 more often than not.
Schools like Florida, Clemson and Auburn straddle the "near helmet/helmet" line. I think the relative lack of history and/or consistency keeps them from being on the highest pedestal, but they could be there with a sustained run of dominance (i.e. NY6 Bowls and Playoff appearances at least 7 years out of 10). Of those, I think Clemson has the easiest path to get there, but I wouldn't count on Dabo sticking around forever. Nick Saban isn't getting any younger, and if Mama doesn't call, the NFL might.