Senate Democratic leader Harry Reid has scheduled a vote Tuesday on whether to proceed with debate on the measure this week.

Some Senate Republicans intent on debating spending cuts and raising the debt limit could upend Reid’s plans and vote against going forward on the Libya legislation. The Senate abandoned its recess week to deal with the unresolved financial issue.

The Libya resolution sponsored by Sens. John Kerry and John McCain has strong bipartisan support in the Senate.

Not so in the House, where last month lawmakers overwhelmingly rejected a similar measure but stopped short of cutting off funds for the operation.