At least $20 billion in PPP loans have been canceled, partly over confusion about the rules.
The House measure would give companies much more time to spend the money and still qualify to have PPP loans forgiven.
Many small companies say they are struggling with the narrow criteria to turn PPP loans into grants.
An architect of the Paycheck Protection Program is pushing for a quick Senate vote on extending it.
The deadline to return PPP loans without penalties is just days away.
The prohibition also applies to private-equity firms.
New guidance was issued after small businesses complained that large companies and big chains were getting loans.
Many firms that have applied for assistance will not get help unless more relief is funded.
The relief package for small businesses is a key piece of a $2 trillion stimulus package.
The former New York mayor has enjoyed a surge in polling numbers heading into tonight's Democratic debate.