For Christmas of 1993, Bandai America didn't anticipate the hype of Power Rangers or how popular it was going to be and only had a few factories, and had short supply in America at the time. I remember being in the lines at Toys R Us or Service Merchandise and people wanting for the Power Ranger toys or buying them super expensive. Some people would buy them and sell them more expensive, one gave me a business card, they were just scammers, I didn't buy anything off him. One day my mom and me went to one store and they only the Battle Bikes and we went back home. The next year, I remember there was a mob grabbing toys and one kid only got a red thunder bike and was sad.
Jingle All The Way came out in 1996, but was inspired in ways by the mania that was Tickle Me Elmo and Power Rangers. The toy the boy wanted from Arnold Schwarzenegger was Turbo Man, a cheaper parody version of Power Rangers. There were even some different colored critters as well.
Toy Story came out in 1995, I doubt they were specifically thinking about Power Rangers but one news article mentioned the Power Rangers and the christmas mania and their furtistic-look being similar to Buzz Lightyear and the movies' point of 'space toys' being more popular. In the sequel Toy Story 2, the Tour Guide Barbie mentioned that the toy producers of Buzz Lightyear were 'short-sighted' by making too few toys for Christmas, echoing the Bandai America fiasco.