He's not a Hall of Famer.
I'd say the no-doubt better QBs of his generation were
-Peyton Manning
-Brady
-Rodgers
-Brees
so there's at least 4 guys in his "cohort" ahead of him.
He's sitting in that second tier of guys like Phil Rivers and Big Ben. Basically, the guys with rings in that tier will probably get in, and the guys with rings won't. Eli and Ben have their tickets punched, so that's 6 QBs from the same era getting in. I don't think they'd go to 7 or 8, especially when Rivers and Romo don't have any playoff success (despite that being a team thing and not a player thing, it weighs in heavily with the Hall voters). Romo didn't have insane counting stats or great longetivity, so there's no real selling point to him. I just don't see any way he gets in over the half-dozen players ahead of him.
Players like Romo are the exact reason the Ring of Honor exists: so teams can give some respect to players who were franchise greats but not necessarily all-time league greats. I have no doubt he'll end up there eventually.