If a government can convert a 1k outlay into 1.1k of tax revenue that same month you aren’t actually paying for those benefits you are getting a little revenue instead of zero revenue. Due to their debts operating across such long timescales people make the same basic argument for things that take longer to see positive returns, but daycare is a very short loop.
Given New Mexico's tax rates, it seems like it would be difficult to do so.
It looks like the program will cost about $600M next year. In order to generate more tax revenue than it costs, it would need to increase personal income somewhere on the order of $12-15B of personal income, taxable sales, business profit or some combination.
Now, a fraction of that will come from the childcare workers. Some may come from stay-at-home parents or parents working part time going to work, but given they say it'll save on the order of $12K/year/family, a family would need to increase their income by about $260K/year in order to pay $12K in extra state income taxes.
It's rare to see spending programs actually pay for themselves. Mostly when politicians talk about a program paying for itself, they preform verbal slight-of-hand, arguing that $x will come back as $x*y in economic activity. That is, of course, a lie, but no one calls them out the fact that economic activity ≠ taxes.
Now as a low population state implementing this at the state level means most of that federal savings/revenue helps people outside of the state, but that’s the issue with implementing such programs at the state level rather than an issue with the type of program itself.
I doubt many people would say they want to raise their taxes to cancel program X because it also helps people they don’t like. You could be right, but I think the more logical conclusion is they are simply being misinformed.