You can only get 80 perks total, so no, you'll be at level 81 with 80 perks.
Yeah, I kind of wrote my previous post wrong. And you're correct.
The game guide I purchased says: "You can level all your skills to 100, which eventually takes you to around level 80. As you're only able to choose one perk each time you level up, and there are well over 200 skill-base perks, don't fixate on obtaining every single one as that's impossible. Instead, focus improving the skills you're most interested in, and ignore perks you won't take advantage of, even if they're in a skill you use constantly." (quoted from the Official Game Guide, page 12, General Advice on Improving Skills.
This is from the Elder Scrolls Wiki: "There are 251 perks in Skyrim. Players can choose one perk per level."
But I think the Elder Scrolls may not have that correct, I still remember 240 from somewhere - memory not too good lately lol.