After months of deliberations, President Obama reportedly will unveil his new war plan for Afghanistan early next week in a prime-time Oval Office address that could come Tuesday evening.

Obama’s decisions on whether to significantly intensify the war effort with tens of thousands of additional troops, as requested by his top military commanders and advisers, were finalized during a long White House strategy session Monday night, White House officials said.

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The top U.S. commander in Afghanistan, Gen. Stanley McChrystal, devised a new counterinsurgency strategy for the war this summer and has requested some 40,000 more troops that he believes will be needed to carry out that strategy. At present, about 68,000 U.S. military personnel are deployed in Afghanistan, and military commanders have said that is not enough to reverse the spreading Taliban-led insurgency.

McChrystal and U.S. Ambassador Karl W. Eikenberry, the top U.S. envoy in Afghanistan, are expected to testify before Congress next week. Politico first reported this morning that the White House is planning an Oval Office address Tuesday to roll out the new Afghan strategy and to reveal the level of commitments in troops and money to support it.

Obama faces powerful skeptics on Capitol Hill, including House Speaker Nancy Pelosi and Senate Armed Services Committee Chairman Carl Levin. Several other Democratic lawmakers, including the chairman of the powerful House Appropriations Committee, Rep. David Obey of Wisconsin, have said a “war tax” on the wealthiest Americans would be necessary to fund an expansion of the war.

Public opinion polls indicate that a majority of the American public, initially enthusiastic about the now eight-year-long war, no longer believe the war is winnable. Keenly aware of this turn in Americans’ mood, presidential aides said that the main focus of Monday night’s strategy session at the White House was on examining the “exit strategy” for each of for options under review, a detailed projection of how long the troops would stay and under what conditions they could be successfully withdrawn.

The president’s Oval Office speech will be aimed at defining the precise U.S. goals in Afghanistan and persuading the nation and Congress — particularly reluctant members of his own party — that the goals are achievable within a set time frame