So, what is "tax liability" for this purpose? For example my DD and SIL get Child Tax Credit and Earned Income Credit which completely eliminates their tax liability. Does this mean they don't get the $1200 each? Do they get $600 each? Crazy. People with families making $50K are exactly the types of people that need this money the most.
Tax liability probably means the number that's on line 16 of your 2019 1040. That's after the Child Tax Credit but before the Earned Income Credit.
If this is a refundable credit, it doesn't really matter though. You would get it even if you had no income and owed $0 tax. If it's a non-refundable credit, then it will show up on line 13b along with the Foreign Tax Credit, and it will not reduce your taxes below $0.
We need to see what is in the bill that actually passes and gets signed into law before we'll know for sure.