Senate Majority Leader Bill Frist set up a possible vote for late this week on a proposal to build a fence along part of the US-Mexico border.
Frist made the procedural move late Monday despite shaky support among some senators within his own party.
But the fence may take a back seat to the more pressing issue of detainee treatment.
If Democrats agree, the Senate would debate detainee treatment first and a vote on the border fence could happen Friday.
Democratic leader Harry Reid of Nevada said he believed he and Frist could work something out.
Congress is scheduled to leave at the end of the week for the November elections.
Meanwhile, key Republican senators remained opposed to the House proposal on the fence.
The House has approved the fencing, but has not funded it. Work also was ongoing this week on the spending bills to pay for homeland security programs.