Senators Joseph Lieberman, I-Conn., John McCain, R-Ariz., and Lindsey Graham, R-S.C., on the Senate floor today criticized as insufficient the Obama  administration’s reported plan to keep 3,000 – 4,000 American troops in Iraq after the deadline for withdrawal at year’s end.

While noting that there’s been no confirmation of  troop levels by the administration, the three senators  said the reported number is “dramatically lower” than what military leaders have said is needed to support Iraq.

The  US military continues to work under the assumption that they’re going to draw troops down to zero unless US-Iraqi negotiations lead to a revision that will allow a certain number of troops to stay beyond December.   But there’s also been the expectation that Iraq will need some US troops to remain to continue training of its forces, and the US military wouldn’t mind keeping troops for counterterror missions.

Iraqi PM Maliki said last month that he’d like to enter into negotiations, but there’s no telling when they’ll begin.

“Three thousand troops is dramatically lower than what our military commanders have repeatedly told us on multiple trips to Iraq that would be needed to support Iraq’s stability and to secure our mutual interests that our two nations have sacrificed so much to achieve,” McCain said today.  ”Our military leaders on the ground in Iraq have told us that in order to achieve our goal, which is a stable, self-governing Iraq, that’s a partner in fighting terrorism and extremism, they need a post 2011 force presence that is significantly higher than 3,000 troops.”

Sen. Lieberman called the plan for 3,000 troops or just slightly higher “shortsighted.”

“If it’s really only 3,000, they are not going to be able to do the job that needs to be done, and not only that, they are going to send a message of weakness, lack of resolve, anxiousness to get out to the Iraqis’ enemies and ours in the region, and that particularly includes Iran,” Lieberman said. “I don’t want us to squander what we have won, and we will, I’m afraid, if we only leave 3,000 American troops there.”

Graham urged President Obama to listen to his military commanders. “I’m not commander, but I can understand why the president would say that’s a bridge too far. I know what the generals have recommended. It goes from the mid teens to the mid 20's, but somewhere north of 10, given my understanding of Iraq I think will work. And I know we’re broke, but the one thing I can tell you we can’t afford after all this investment is to lose.”

Traveling in New York yesterday, Defense Secretary Leon Panetta was asked about the report and the concerns by US personnel over reducing troop levels in Iraq.

“With regards to what our presence will look like on that, that is going to be a subject of negotiations with Iraqis,” Panetta said. “As I said, I can’t give you a number or tell you what that number looks like. It’s going to have to be part of the negotiations.”

ABC News’ Luis Martinez contributed to this story.