Senate Democrats are at odds over what their agenda should be for the next few weeks and when they should be able to go home.

Though Senate Majority Leader Harry Reid suggested Tuesday he is prepared to move forward with debate on the defense authorization bill next week, some of the Nevada Democrat’s rank-and-file Members are not too thrilled with that notion.

Democrats emerging from their first policy lunch since they returned from the August recess said they pushed Reid to keep the focus on jobs and the economy. They also urged Reid to wrap up work this session a week earlier than Oct. 8, the target adjournment date.

“I would support doing anything we can in the next three weeks, and then adjourning,” Sen. Mark Udall said. “I would certainly support adjourning on the 1st. That would enable people to campaign hard, make their case, Republicans and Democrats alike. I think that’s where the sentiment of the caucus is at — if we can adjourn in three weeks, let’s do so.”

As for the agenda, the Colorado Democrat added, “I think it’s a very fluid situation right now when it comes to what we’re going to consider on the floor. We all agree it has to be jobs, tax extenders and tax cuts.”

Reid, however, seemed to be trying to thread a needle on the agenda. Senators pressed him to hold votes in the coming weeks on their pet issues or issues they believe will be politically beneficial for the party. For example, Reid announced to the press that he would add the DREAM Act to the defense bill. The measure would give illegal immigrant children a path to citizenship if they go to college or join the military. Reid also told Senators privately that a proposal to end secret holds would be offered to the defense measure, according to CongressDaily.

One senior Senate Democratic aide indicated that rank-and-file Senators’ desire for a three-week session may not be possible if Senators want to debate the Bush-era tax cuts and pass a stopgap spending bill to keep the government running without clearing regular appropriations bills. “We’re probably going to be here going on four weeks,” the aide said.

Part of that time will likely be used to devise a cohesive strategy on how to deal with extending tax cuts for the middle class while letting rates on higher earners go up. Reid declined to outline a specific game plan on the tax-cut issue but said the it would come up before the elections.

Senate Minority Leader Mitch McConnell reiterated Tuesday that his 41-member Conference is opposed to letting taxes go up on those in upper income brackets, including on some small businesses.

“What we ought not to be doing is raising taxes on anybody in the middle of a recession. We know that there’s bipartisan agreement with that,” the Kentucky Republican said Tuesday during a news conference.

Reid said Senators would have a choice to “take care of the middle class” or to “take care of millionaires.”