Senate Majority Leader Bill Frist set up a possible vote late this week on a proposal to erect fencing along a third of the U.S.-Mexican border.

Frist, R-Tenn., made the procedural move late Monday despite shaky support among some senators within his own party.

However, the fence may take a back seat to the more pressing issue of detainee treatment, which Frist attached to the fence bill.

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 to erect 700 miles of fence or said they wanted changes to the bill.

"I'm concerned if we do this then will be no more interest to do the broader bill," said Sen. Mel Martinez, R-Fla., referring to the now stalled Senate immigration bill that he helped write. "I'm still weighing it."

Martinez said he might support the fence if it were the same size as one already approved by the Senate.

The Senate included 370 miles of fence in the immigration bill it approved in June and provided $1.8 billion to build it. But that bill stalled amid heavy opposition from House Republicans.

Sen. Arlen Specter, chairman of the Judiciary Committee, criticized the House's unwillingness to negotiate a comprehensive immigration bill, saying the House "doesn't think much of the bicameral system."

"There ought to be a fence along a good bit of the heavily populated area near Tucson, near San Diego. And I'm for that fence. But I'm not for the fence piecemeal," Specter, R-Pa., said in a speech at the National Press Club on Monday.

Sen. Larry Craig, R-Idaho, also said he had not decided whether he could support the measure. He wants to add to it a measure helping provide more laborers to farmers and the agricultural industry.

Meanwhile, Sens. Kay Bailey Hutchison and John Cornyn, both R-Texas, were lobbying to amend the measure to allow local border officials to help decide where fencing should go.

"Everybody wants the same thing, but we do also want commerce and we want business to keep going and we want effective border security," Hutchison said.

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.