Citizens for a Nuclear Free Iran launched a nationwide ad.
McCaskill said it would be "more dangerous" to reject the agreement.
The hard-line proposal is rekindling debate on an issue that has long vexed the GOP.
The Massachusetts Democrat said Iran getting a nuclear weapon is a "serious threat ... to all of humanity."
The Texas Republican suggests that has been his position for years.
But the senator says the U.S. hasn't done enough to counter Iran's support of terrorism.
Rubio wants to see any letters the administration sent to foreign governments.
The lawmakers want answers on whether the administration was briefed on the deals.
Julian Hattem 08/18/15 01:30 PM EDT
“I hope we can defeat it, but the procedure is obviously stacked in the president's favor."
Democrats want the Republican leader to start negotiations on a budget.