The proposal addresses individual payments, money for schools and unemployment benefits.
A full-fledged GOP proposal is expected later this week.
Nancy Pelosi and other House Democrats voted on Friday to give Americans an additional $1,200 payout as part of the HEROES Act.
The Senate has approved a $484 billion relief package intended to aid flailing businesses. Critics of the bill say it doesn't go far enough.
Congress looks to add another $250 billion to the small-business aid program, as funds from the first wave run out.