Emergency Family Relief Act of 2020 This bill allows a new refundable tax credit for emergency family relief payments in response to COVID-19 (i.e., the coronavirus disease 2019). Specifically, the Department of the Treasury must establish a program for making emergency family relief credit payments on a monthly basis for the period prior to January 1, 2021, without respect to tax liability, for taxpayers with dependent children equal to $1,288 for a two-person household, $1,446 for a three-person household, and $1,786 for a four-person household. For households larger that four persons, the credit amount is $1,786, plus $420 for each additional household member. These credits amounts are phased out for a taxpayer with a modified adjusted gross income exceeding $50,000 ($100,000 for a joint return).