Republican senators are tiptoeing around the possibility.
Rep. Chaka Fattah was indicted last week on bribery and money laundering charges.
A first vote on the long-stalled bill could come on Wednesday.
Two Democrats voted to move forward with the bill, which stalled in a 53-46 vote.
Rep. Yoder's bill is in response to the controversial Planned Parenthood videos.
An article raised questions about Graham's military service.
The Senate will take a vote Monday to move forward with legislation to cut off federal funding.
Manchin is the first Senate Democrat to back the legislation.
"It's time they are investigated," Sen. James Inhofe said.
Republicans need 60 votes to move forward with the bill.