The bill, passed 241-179, would withhold certain federal law enforcement grants.
"We need to figure out a way to phase out this program," Bush had said.
The bill would keep states from issuing mandatory labeling laws for foods that contain GMOs.
The Texan wants to name the street "Oswaldo Payá Way" after a Cuban dissident.
The Speaker said "it’s pretty clear" that a stopgap bill will be needed in September.
Reid's remarks come after Sen. Patty Murray (D-Wash.) pulled her bill from being voted on.
But the administration says it doesn't have the agreements between Iran and the IAEA.
The House bill comes in the wake of a San Francisco shooting that launched a political firestorm.
But the legislation still faces challenges from both sides.
The bill would roll back certain parts of the EPA's regulations on coal ash waste disposal.