There is no question that the Iraq war added substantially to the federal debt. This was the first time in American history that the government cut taxes as it went to war. The result: a war completely funded by borrowing. U.S. debt soared from $6.4 trillion in March 2003 to $10 trillion in 2008 (before the financial crisis); at least a quarter of that increase is directly attributable to the war. And that doesn't include future health care and disability payments for veterans, which will add another half-trillion dollars to the debt.
As a result of two costly wars funded by debt, our fiscal house was in dismal shape even before the financial crisis -- and those fiscal woes compounded the downturn.
And just for shits and giggles, here's Jane Galt in 2003.
The war will certainly cost more than the $60b and change that the President is asking for. But it is not going to run us several trillion dollars (though even if it did, that would work out to less than 0.1% of GDP over the next 20 years.)