Reid, D-Nev., filed a resolution Friday in the Senate and scheduled a Wednesday vote to end debate and move the resolution to final action, The Hill reported Saturday.
Four Democrats have announced they plan to vote against the resolution, which would support President Barack Obama's call for a military strike against Syria.
Obama "has really given him a tough one this time," said Jim Manley, a former senior adviser to Reid.
"If this vote were to fail," Manley said, "it will have huge consequences not only for the president's domestic policy but also his foreign policy and for the people of Syria."
"This is about as high stakes as you can get," he added. "How's Iran and North Korea going to react to a defeat? How are House Republicans going to deal with the debt limit?"
A senior Democratic aide said "double-digit Democrats" would probably vote against the resolution.
Anna Galland, executive director of activist group MoveOn.org Civic Action, which has been lobbying against U.S. military action in Syria, said she expected opposition to grow among Senate and House Democrats by Wednesday.
Sixteen Senate Democrats and eight Republicans already said they plan to vote for the resolution.
Reid has said he expects the resolution to pass.