The bill heads to President Obama's desk.
Grassley accused the Senate Democratic leader of holding up GOP legislation.
Sen. Lindsey Graham said lawmakers need to make sure they didn't open "Pandora's box."
The House is expected to vote Wednesday.
Cornyn called the White House detached "from anything to do with the legislative process."
Jordain Carney 09/28/16 01:05 PM EDT
McConnell said the chamber will vote Wednesday afternoon on a CR to fund the government.
Jordain Carney 09/28/16 12:43 PM EDT
The Senate voted 97-1 to override the veto of the Justice Against Sponsors of Terrorism Act.
"I'm convinced that there's going to be help for Flint in the lame-duck."
Julian Hattem 09/28/16 08:46 AM EDT
The Senate will vote to override Obama's veto on Wednesday.
Senate Democrats introduced a resolution to block the chamber from leaving.