Sen. Joseph Lieberman (I-Conn.) dropped a resolution at the end of July, along with Sen. Lindsey Graham (R-S.C.), calling on the Senate to officially recognize the success of the surge in Iraq. Democrats have no plan, however, to let Lieberman and Graham, the Senate’s top two supporters of Sen. John McCain (R-Ariz.), walk off with such an easy political victory and will be introducing their own alternative resolution, Senate aides said. Lieberman was criticized when he introduced his resolution for invoking the September 11th attacks; his recent speech to the Republican National Convention in which he questioned Sen. Barack Obama’s (D-Ill.) readiness to lead the nation infuriated Democrats, leaving them even less likely to allow him to claim credit for the surge.

An opponent of the surge, Obama recently conceded to talk-show host Bill O’Reilly that it had succeeded beyond our “wildest dreams.” McCain has cited his own support of the surge as a testament to his judgment. Yet Obama and Senate Democrats argue that the success of the surge was the work of many more forces than the troop increase and strategy shift advocated and executed by Gen. David Petraeus. Sunni tribes in Anbar province, for instance, turned on Al Qaeda many months before the new troops arrived. The “Anbar Awakening” is thought to have contributed greatly to the decrease in violence. Radical Shi’ite cleric Muqtada Sadr called a unilateral cease fire, further contributing to the decline. And warring Iraqi factions walled themselves off from each other, fled the nation or were killed – also contributing to the downturn in violence.

The alternative resolution has not been finalized, said one aide, and probably won’t be until Sen. Carl Levin (D-Mich.), chairman of the Armed Services Committee, returns to Washington later today.

UPDATE: Lieberman spokesman Marshall Wittmann says his office has not seen nor heard of the alternative resolution.

John Bresnahan contributed to this post.