a 1080p runs a resolution around 1920 x 1080. (this varies a little from tv to tv so check your specs for your tv.)
I game at 1920x1200 on a 24" monitor with a gtx260. Short of Crysis I can max out most games.
Would I like a better card? You know it give me a GTX295 any day of the week.
Can I afford it? No.
Do I really need it? not really. But, If I could afford it I would.
So there is a convoluted answer for you.