First, 2007 wasn't that bad economically (though from what I've heard, many economists had a feeling of impending doom). Second, and more importantly, the Recession ITTL is going to be weaker and delayed. The Bush Tax Cuts contributed massively to a growing economical bubble that would eventually pop. The Wars in Iraq and Afghanistan didn't help in this regard either. Gore's plan basically called for a contractionary fiscal policy (one of his goals was a debt-free U.S by 2012), which changes all the economic cycles we're used to. 2008 is probably happening in 2009 or 2010, and it's going to be a lot less catastrophic.
It seems like a stretch to say the Bush Tax Cuts or War in Iraq led to the financial crisis. I don't think I've read a single economist who has attributed either as a significant contributing factor, though they both obviously impacted the performance of the United States economy.
And a contractionary fiscal policy could actually make the crisis worse. The Federal Reserve significantly cut interest rates between 2001 and 2003 due to fears about the economy (dot com bubble, 9/11, etc) and the possibility of deflation; contractionary fiscal policy may keep rates lower for a prolonged period of time which could worsen the housing bubble.
Though nothing happens in a vacuum. Perhaps tighter fiscal conditions mean an economy that is slower, with less borrowing and deficits, which leads to banks that are more hesitant to lend and consumers less willing to agree to a new mortgage. But that wouldn't really end the easy credit conditions of the early 2000s or the fact that everyone and their grandmother (including the banks themselves) seemed to buy into housing as the sector to invest in.
The most significant thing I think a Gore Presidency could accomplish would be having regulators that take their job more seriously. Suffice to say the Bush White House along with most Bush Officials (especially Greenspan) were asleep at the wheel as the housing sector bubble formed and then exploded, perhaps more prudent regulators could allow someone to sound the alarm before things went so catastrophically wrong in 2008.