My guess is that it would be almost impossible to save 1K/month if your take home pay is only $2K/month. There are minimum requirements for food, shelter, transportation, etc.

A pre-tax yearly salary living wage to cover the minimum in the US would be $45K - $68K depending on location. Let's look at a low end, low cost of living state. $45K pre-tax translates to about $3K per month take home pay. Which means that if you had $3K per month take home, you would just be covering the basics for a family. If you are trying to get by on $2K per month, you're already making some difficult trade-offs to survive.

So, I don't think it's realistic to say someone with $2K per month take home pay can save $1K per month.