re: What would the national perception be if we beat Clemson?

I am an SC fan, but I watched almost all of LSU's games last season. The Tigers were a very talented bunch that could have beaten anybody on their day. It's extremely difficult for a CF team to play at "elite levels" in every game of the season, though we as fans expect it, whether it is a critical conference game against a ranked powerhouse or a not-so-prestigious bowl game against an ACC team. I expect LSU to win at least 9 games this season, good shout for 10 or 11 if fortune smiles on you.
"National Perception" relies on people who remember LSU won titles a few years back, and then went 0-2 in the last two big post-season finales. Those people don't watch week in, week out though, so take it with a grain of salt.
Tl;Dr: LSU's really good, and will be this season. National perception's based on casual fans/observers and ain't nobody got time for that.