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.
Tony Spell went on CNN's New Day Weekend to defend his "stimulus challenge," which asks his followers to donate their checks to the church.
More than 80 million stimulus payments have been sent to American taxpayers. Several million of those were deposited into third-party accounts.