A disagreement between GOP lawmakers over a military detainee amendment has caused a delay in bringing the fiscal 2013 defense authorization bill to the Senate floor until later this week, according to the ranking Republican on the defense policy panel.

Sen. John McCain, R-Ariz., said Monday that the differences between Sens. Rand Paul of Kentucky and Lindsey Graham of South Carolina were minor and should be cleared up. But McCain acknowledged the dust-up had delayed consideration of the bill (S 3254).

“We have a small problem, but we’ll work it out,” he said.

Late Monday, Senate Majority Leader Harry Reid, D-Nev., made a motion to bring the bill to the floor, but debate was put off until Tuesday. The bill is now expected to reach the Senate floor by Wednesday, aides said.

McCain learned of the issue as he was headed to the Senate floor earlier in the day to rebuke statements by Reid that Republicans were disagreeing among themselves and that was why the bill was delayed.

He huddled with the Republican and Democratic staff directors of the Senate Armed Services Committee and then said it appeared Graham had some concerns.

Sen. Carl Levin, D-Mich., chairman of the Armed Services panel and manager of the defense bill, said that after meeting with Reid earlier Monday, he was “optimistic” that the bill would make it to the floor.

Paul’s amendment would insist on the protection of a citizen’s Sixth Amendment rights when captured or arrested in the United States and detained by the military in relation to terrorism. Paul wants to ensure the right to a speedy, public trial before an impartial jury and that the accused is informed of the nature and cause of the accusation, can confront any witnesses and has a process for obtaining defense witnesses and counsel.

A senior GOP aide indicated late Monday that Paul and Graham have not yet sorted out their differences over the amendment, but Graham has agreed not to block a motion to proceed to the bill.

McCain and Graham each object to Paul’s amendment. They argue that there has been enormous amounts of debate on the handling of the detainee issue and that these are settled issues in law. Paul’s amendment would add a new wrinkle.

The senior aide said Graham and Paul would continue to discuss the issue.

Levin also raised concerns about amendments he was being presented with that were not germane to the defense policy bill. He would not describe what was being proposed.

“We have to finish this in three days,” Levin said. “These amendments have nothing to do with the bill.”

Senators still hope that the overall bill could be passed by the end of the week. But aides said passage is more likely to occur Monday barring further disagreement.

Reid attempted before the Thanksgiving recess to seek approval of a unanimous consent agreement that would have limited bill debate to only germane amendments. That agreement was blocked by the GOP.

At that point, it was left to Levin and McCain to manage the amendments, attempt to limit their number and pass a bill that has been enacted every year for the past half-century.

The House passed its version of the bill (HR 4310) in May. Lawmakers must complete the defense policy bill, then complete a House-Senate conference, adopt the conference report in both chambers and send it to the president before the beginning of the new session of Congress in early January.

Megan Scully contributed to this report.