Kotatsu Heater

So, we purchased a good transformer; PowerBright VC1000J Step-up/Step-Down Voltage Transformer for Japan (1000 Watt Capacity) to operate our Kotatsu table in the US, but the heater still will not operate. We initially tried to see if it would work on US power, but it would not. I don't imagine that the power coming from a US outlet would have damaged the heater. Is this possible?

Hard to say. Is it a basic lamp heater or a fan heater? If it is a lamp kind, did it momentary lit when you plugged in initially direct to US outlet?

Hello,
If you plugged it with the 120V 60HZ it mean you plugged with 20%+, but, if the kotatsu is marked only 100V 50HZ (instead of 60Hz) you reached the top difference which corresponds, as you plugged a with 135V. Therefore you may had burn something since the difference is 35% + while tolerances for electricity differences are commonly 10%+/10%-.
If it is the lamp type, the lamp will brake and you will do not feel any burned smell. If is the fan type you may had burn the fan and/or the resistor and you will feel burned smell.
Even you had some burning smell, and especially if it is the fan type, more likely you broke only the internal fuse. Therefore you should open the lower metal cover, find/check the fuse and replace it (even it looks OK) with a new fuse of the same Ampere. (It is quite easy)
After that you should try it only with transformer 100V side.

At the end if you really burned it, even is the fan type you can easily buy (eg. at Rakuten.co.jp) a new bulb, or the full fan resistor box which is not too expensive, and not heavy for international shipment.

It all depends from my experience.
I have a Panasonic toaster oven, soldering iron, table lamps, etc. I bought in Japan & some are over 40 years old and still working w/o any transformers. Even the lamp bulb lasted normal.
Where in Japan did you buy, in Tokyo? If so 50Hz motor vs. 60Hz in Nagoya and west or in US if fanned but it would just run a little faster. Any electronic circuit inside? Without any info. no can help.

For the previous one.
You are correct. All item you mentioned are not harmful as a kotatsu to set up fire in your house. If you ad the blanket now mostly synthetic fibers.
"I have a Panasonic toaster oven, soldering iron, table lamps, etc. I bought in Japan & some are over 40 years old and still working w/o any transformers. (electric items only ... when you ad a motor is electromechanical, when you add circuits or E.C. its electronic)

More you go in the past more you find highest +/- tolerance.

If your items are 40 years old, you should know that year by year the international standards lowered tolerance to avoid a list of problems... (on the other hand they highlight the allowed international use and range. WW)

The id poster will enjoy you sending your old Japanese toaster to put under their table to work as the kotatsu heater.