Things will depend on the type of dwelling you desire and amenities.

The $80K per year won't be bad for New Mexico, but it's not going to be outstanding either. If you were single that would be fine, but caring for three others will zap it from you in my opinion. Maybe I have high standards, but this is how I think things will roughly be for you.

Mortgage/Rent UK: £700 US:? Figure 3 Bed Home/Apartment $1200 USD
Council Tax £140 Not sure how this translates to the US
Gas £60 If this is based on a month then you're screwed as prices will be around $3.80/gallon and I suspect you will drive about to see the area so figure you'll spend about $240 for the first few months and then drop it to $160 per month.
Electric £60 This will fluctuate on the seasons. As mentioned above New Mexico in many places is high altitude and can get cold. I own a home in the State of Colorado and would pay around $40 during the summertime, with no air conditioner running and then up to $140 in the winter with gas furnace going as the temps drop below freezing in the night.
Phone £30 You will most likely have a hard wire land line for local calls $40 per month. Mobile phone I was paying about $50 per month with only 400 minutes (incoming and outgoing as stated above)
Internet (ADSL) £30 Will vary on the type of service. Dial up $30 or Cable High Speed $45. It will be fast enough for you.
Water Rates/Meter £50 Typically billed every two months and I paid $25 Wastewater, $15 Usage in Gallons <3,000gallons, and a few other fees maybe total $10. Keep in mind I'm single so add in the three others and your usage goes up, however it's not going to crush you because your fee will not double.
Food Shopping £500 All depends on you and the family here. Figure $700 for a single guy per month and this would include going out a few weekends too. The price of milk, eggs, bread, and other staples has risen sharply.
Life Insurence £26 Could possibly be free or included in your health insurance package. If free it wouldn't be anything significant. You'll see advertisements on television there, but don't get sucked in to those deals.
Mobil Phone £30 See above, but figure your girls and wife may want them too. Cricket can provide local call service and this is not very expensive, but no calls outside of the area code can be dialed.
SKY TV (Cable) £47 You'll most likely want the full package in order to watch EPL matches (early in the mornings too baby, but live). You will want a few specific channels FSC (Fox Soccer Channel) and Gol TV. EPL, Italian, French, Spanish, and German matches will be available on these channels. If you get into Mexican footy those matches will be local access channels in Spanish later in the mornings on Saturdays and Sundays. Cost will put you around $100 per month. But look to combine this package with mobile phone and internet and the companies will give you a better rate, plus you can have one lump charge to your credit card rather than multiple charges.
TV License £13 You'll be charged taxes and other fees in the TV Cable bill, see above.

I'm not sure what your clothing supply is like, but because of the cool temps in winter figure in a few jackets for everyone and other clothes.

Don't get wrong, it could be a great experience. If your wife can work that would help a lot, but the $80K doesn't seem like much for a family of four in my opinion. She could probably add an extra $20K per year, but I don't know how the work visas are set up. I know the information exists on this forum for your situation.

As stated above figure 30 percent taken out in taxes, which includes federal taxes, state taxes, and a few other items. You should have a tax accountant at the beginning of February help you file the taxes and chances are you'll receive some money back from the federal government and state government. If you owned a home you would receive a bit more because of deductions on interest payments and whole different topic.

Factor in purchasing a vehicle or two. Depending on your preference it could be costly. Let us know what you drive now and what your expectations would be in the US. You can find used/pre-owned autos for decent prices, have a mechanic check it out first. If you decide to go start another thread and things can be discussed in more detail if you think you might be getting taken.

Don't choose the place based on the web. You will want to be closer to the larger cities for schools and activities.

If the company offering you a position doesn't offer health and dental insurance, tell them ToGoF***Themselves. No excuses from companies not willing to put people on a health plan. If you smoke it will affect your payments. Deducted from a weekly or bi-weekly paycheck.

Best wishes.