Yes, as of August 1st unless the US government changes their mind or delays the rule. At least one rabies shot that has not expired (they are usually good for 1 or 3 years depending on the shot). Finding a vet in Mexico that can install an ISO certified chip, administer an approved rabies vaccine AFTER the chip AND have it signed off by a government veterinarian is where you will probably run into a brick wall.

I think the best option is to get your dog to the US before August 1st, get an appointment with a USDA certified vet, and have the chip and vaccine administered and recorded with the USDA. You will then be good for as long as the rabies vaccine is rated (so ask for the 3 year shot).

You will still need to fill out a form online every time you cross into the US with your pup.

Personally, I think this is way overboard for accepting animals from countries with almost zero risk of rabies but there are lobbyists in Washington pushing for this. Drug companies, chip makers, American Kennel Club, etc.