You can’t even carry one duffel bag unchecked on a budget airline anymore, unless its a very small one. Some of the cheaper airlines even charge extra for overhead luggage.
That might be true for domestic US flights, which I don't have experience with, but every airline between US and Mexico, or inside Mexico, has an option for 1x carry-on and 1x "personal item" where the personal item just needs to somewhat fit under the seat in front of you.
This goes for Mexico's budget airline Viva Aerobus too.
