Sen. Chris Coons said Congress must pay for the fight against ISIS.
The Budget Committee leader said the chamber has taken 17 votes in more than six hours.
They unanimously backed sanctions if Obama can't verify that a deal is being followed.
The Senate is voting on amendments to the GOP budget.
Sen. Blunt said his amendment would "send a clear message" to the administration.
The bill would apply to detainees released after Feb. 1 of this year.
Sen. Scott said his amendment would raise awareness about a tax on premiums.
Only a small group in the House opposed the $200 billion legislation.
Senators backed year-round Pell grants for college students, but rejected a funding increase.
Senators rejected the measure in a 45-55 vote.