Don't know what an RCA cable is, but there is probably a way to hook up your NES to a plasma TV. I have an SNES hooked up to mine and it works fine, so yours should work. You might need some sort of cable converter, though.
As long as the HDTV has Red/White/Yellow cables on it, and you have a R/W/Y cable with the trio of 'em on each end, then you're good. Also, if the yellow one is missing on the TV but you have R/G/B, plug the Yellow into the Green. If you don't have one, you could always go to an electronics store; the NES might come with the cable, anyway.
Here's the cable:
As you can see, the NES only uses the Red and Yellow cables.
Simply hook up the Red and Yellow to the corresponding inputs on the HDTV. If you're missing the Yellow, like mine, then plug it into the Green on the R/G/B input. Also, the White doesn't need to be inserted, since the NES doesn't use the White.
BTW, for some reason, this image kept flipping itself when I uploaded it to imgur, so it might be stretched or squished.
^Good post. And if your TV doesn't have the correct plugs, you can always find things like converters. Or if anything plugged into your TV already has the RWY cables, you can plug it into that device. (Example: DVD player. You can plug your NES into your DVD player if your DVD player is attached to your TV.)