Yes, a check for $2000
Usually there are phaseouts on credits, think of them as a reverse tax bracket... so it may be like, for every 1k over 10k you make, you'll get $100 less of a credit, so at 30k income, you get nothing... NOTHING, GOOD DAY SIR.
The best example of a credit is the Earned Income credit. Googling that will give you a ton more information on tax credits. The theory behind that credit is that if you make between like, 10k-25k (those values arbitrary... been years since I've looked it up), you'll get money back. The theory behind it is that if you made less than 10k, you're likely a student, child, etc, and shouldn't get money back. It's also earned income, so that's income subject to payroll taxes, not investment income or partnership income (which are considered passive forms of income).
Yes. Or budget out the excess that they receive in April for the year. But there would be the initial sting upon implementation.