This is something to experiment with. I'd still go for NiCad batteries, simply because they are very tolerant of abuse, and this is really abusing the cell
Get yourself some nichrome wire and determine what length is required to *just* start to glow a little. Start with a long piece of wire and make it shorter and shorter until you find the right length.
You can get more than you'll need very cheaply on ebay:
http://shop.ebay.com/?_from=R40&_trksid=p3907.m38.l1313&_nkw=nichrome+wire&_sacat=See-All-Categories (and probably from other places too)
I have no idea what gauge you would need, or a ballpark length. Once you've found the right wire size and length you should measure the resistance and the voltage across it when operating. Then use ohms law to determine the current.
I'd start with the smallest gauge of wire as that will give you the lowest power consumption, and consequently the ability to use the smallest battery. Be aware that the "correct" length will change depending on the type of battery you use, the size of the battery you use, and how easily the heat can radiate away (so winding the wire into a tight spiral will make it hotter because heat can't escape so fast).
A quick glance at some specs indicates that 32 SWG (0.27mm diameter) has a resistance of about 20 ohms per metre. If we assume that 6A at 1V is the highest power we can take from an AA Nicad, then the minimum length of this gauge of wire would be about 8 cm would be the minimum length. That seems too long to coil up without risk of shorting, so maybe a smaller gauge would be better. You do have to be careful that the wire heats up and doesn't act as a fuse. Winding a longer length around a ceramic sheet of some type, or making your own stiff coil may be an option.