With 59 Senators publicly voicing support, the hunt's on for the 60th vote to advance the measure before a critical vote Tuesday.
The issue has taken centre stage in the waning days of this Congress in hopes it will boost the prospects of Louisiana's Senate candidates.
Democratic Sen. Mary Landrieu pushed for the Senate vote. Her rival, Republican Rep. Bill Cassidy, sponsored the bill the House passed late last week.
All 45 Senate Republicans support it, along with 14 Democrats.
The White House has issued veto threats of similar bills.