The “war on terror” itself has not been the driving force behind much of the country’s difficulties. It certainly opened the door for the Iraq invasion, which (IMHO) absolutely would not have happened if 9/11 had not happened. I think the current administration would have gone a long way toward moving us to the point where we are now anyway, only without the loss of life and capital spent on Iraq.
One of their first moves was to withdraw from the Kyoto agreement, which illustrated their philosophy of unilateralism, and started the process toward alienating the rest of the world. Their disdain for government in general led to the lack of financial regulation that has led (in large part) to the current financial crisis, as well as the Katrina response debacle. Even though they generally spout (or spouted, prior to getting their hands on the purse strings) the mantra of smaller budgets and government, the approach of cutting taxes while allowing Congress to run wild with spending for their favorite causes would have demolished the budget surplus and put additional pressure on the economy regardless of whether 9/11 had happened or not. I’d have to look to make sure, but I think the budget was on a trajectory to go from surplus to deficit prior to 9/11 due to the massive tax cuts that happened early on in the administration.
9/11 and the response (including the Iraq war) have certainly exacerbated these issues. But I think the root causes were already inside the White House and Congress before the attacks started.
(ETA): I do think Al Qaeda believed (wrongly) that the attacks on the World Trade Center would critically damage the economic strength of the country. Had they really known what they were doing relative to damaging the US economy, they’d have flown those planes into the largest refineries they could find.