Lawmakers from both parties have been complaining loudly over the costs of sending tens of thousands more troops into Afghanistan — a strategy that President Barack Obama will spell out in a Tuesday night address. But the reality is that Congress won’t have to approve any new funds for at least another six months.

Obama won’t need to ask Congress for more money to support his Afghanistan war strategy until “late spring at the earliest, maybe May or June,— a senior House Democratic aide said Monday.

It is unlikely that Obama would try to add money to the fiscal 2010 Defense conference report, which is set for a vote in December. In the meantime, “there are probably enough funds— from the fiscal 2010 ‘supplemental’ to get the president through,— said a Democratic aide familiar with military funding levels.

White House Budget Director Peter Orszag has estimated that each additional soldier in Afghanistan could cost $1 million annually, for a total that could reach $34 billion if an expected 34,000 more troops are added.

Beyond additional funds, aides said to expect the Pentagon to reprogram some of its current funds to pay for Obama’s Afghanistan strategy. Former President George W. Bush took this tack several times when Congressional Democrats refused to provide him with more funding for the Iraq war.

The timing of a vote to give — or not to give — Obama more funds to carry out his Afghanistan plan depends on several variables, including the number of troops he requests, whether Iraq troop levels are decreased and the equipment needs of the additional troops.

Speaker Nancy Pelosi (D-Calif.) has said repeatedly that House Democrats lack the appetite for sending more troops overseas. But some are already signaling support for spending more in Afghanistan if the effort is tied to withdrawing military forces from Iraq.

“We’re paying for this. At the same, we’re reducing money we’re spending in Iraq … We had no business being there in the first place. But we did have a necessity to go into Afghanistan to stop the kind of attacks al-Qaida engaged in,— Rep. Maurice Hinchey (D-N.Y.), a member of the Appropriations Subcommittee on Defense, said on MSNBC.