1080p on 720p Display?

I'm about to buy a new TV, and i'd love to get a 1080p TV over 720p... However, the size i'm looking for is a 32"--and there aren't too many 1080p displays under 37" on the market--meaning i'll most-likely be buying 720p.
I'm wondering, what happens with a 720p LCD, and a 1080p source?
Most of the TVs i see are 720p resolution--period. Although i've been looking at a Toshiba the [32HL67]... and Toshiba boasts that it can accept 1080p signals-as a 720p display. My main question is, what does that mean in comparison to other TVs, like the Samsung [LN-T3242H]? What does the Toshiba do with that 1080p signal as opposed to the Samsung? Downscale...?

My Top Picks, as mentioned in my question.
http://www.bestbuy.com/site/olspage.jsp?...
http://www.bestbuy.com/site/olspage.jsp?...

Answer:
itll show up at 720, which still looks great btw
It will downscale to 720p or 1080i.

Sharp does have both a 37" and a 32" LCD tv that are both 1080p resolution. I believe the regular retail price of each is 1599 for the 32 and 1799 for the 37.

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