I think your wrong here. Brees was highly criticized until he won a SB. Don't get me wrong. Bree's is an awesome QB, but the naysayers ran away after he won. I think the same would happen for Romo.
Brees had a different career though. If my memory serves correctly, Brees was thought to be somewhat of a bust, which is why San Diego spent the 1st overall pick (4th after trade) on Phillip Rivers. You wouldn't spend a top 4 pick on a QB if you already had a good, relatively young QB. I know Brees had injury issues as well (which is why Miami didn't sign him after he left San Diego). But I remember San Diego thought he was a bust so they drafted Rivers. Then his last season with them (which was Rivers rookie year) Brees played unbelieveably.
Romo, on the other hand, was an undrafted free agent, came out of nowhere to become starting QB for the Cowboys, then consistently choked in big moments. If you remember correctly, everyone was in love with Romo his first season as a starter. He only played a little over half the season and still made the Pro Bowl by a landslide (his only Pro Bowl, I think). Then, he brings his team to the playoffs and bobbles a field goal snap in a loss to Seattle. I think everyone felt bad for him after that, but then it happened again, and again, and you know the rest. I think, the way people are, they just started enjoying seeing Romo fail in humiliating fashion. Since then he's had this stigma as a choke artist. It also doesn't help that he plays for the Dallas Cowboys.