The bill unexpectedly imploded last night after the House required a two-thirds vote to pass it.
This new strategy could require a simple majority.
The Rules Committee announced an emergency hearing on Wednesday on provisions of the legislation, which if not renewed, are scheduled to expire at the end of the month.
Anticipating eventual success, Kentucky Sen. Rand Paul released a statement Wednesday saying he would oppose the bill in the Senate.
"I firmly believe it is a primary duty of our government to do what it can to protect the lives of its citizens. But I also believe it must in equal measure protect our liberty, and in this our government has failed us. We should remember the words of Ben Franklin, who famously said ‘Those who would give up essential liberty to purchase a little temporary safety deserve neither liberty nor safety,'" Paul said.
