I am going to somewhat disagree with this. During a recession people eat less steak and more macaroni and cheese. They shop at Walmart more and other more expensive stores less. People choose cheaper substitutes during a recession.
In 2008, the stock market crashed. The Wii continued to dominate throughout 2008-2009 while PS3 and XBox360 sales were sluggish. At the same time the cheaper DS was also dominating the PSP. In both cases people were choosing the cheaper substitutes. So, it does not appear that the recession caused anyone to leave the gaming market, quite the opposite in fact. However, the recession did correlate with the success of cheaper substitutes.
While the recession "officially" began in Q1 2008, it took a while for the effects to be fully felt. Unemployment grew only slowly at first, not accelerating until the second half of the year and on into 2009, where it peaked at 10% in October that year. Unemployment remained over 9% through 2011, and by time the current console gen began it had just finally gotten below 7%.
The 360 and PS3 both had unimpressive starts, and that was before the recession. Despite no real competition for most of the year and a still-healthy pre-recession economy, the 360 sold only 3.93M units in the U.S. in 2006. In 2007, still pre-recession, it had jumped to 4.62M, an increase of only 17.6%, and that's despite a $50 price cut and the release of Halo 3. The PS3 sold only 2.56M in 2007.
The PS3 experienced steady growth with each successive cut to its initially very high price tag, with the most growth coming with the PS3 Slim, the first SKU regularly priced at $300, which was released right when unemployment hit its absolute peak.
While the 360 was mostly flat from 2007 to 2009, that could just as easily be chalked up to the RRoD issue preventing possible growth. The "Pro/Premium" SKU (the cheaper of the HDD-equipped SKUs) had already been permanently slashed to $300, only $50 more than the Wii, by Sept. 2008 when unemployment was quickly en route to its peak. It didn't experience significant growth until the 360 S was released in June 2010. That model, unlike the PS3 Slim, was not also a de facto price cut on its own (meaning the regular price of the base HDD-equipped 360 models never dropped below $299 after Sept. 2008, nearly two years before the S-model was released), but it did resolve the hardware issues plaguing older models of the 360. Both systems peaked in sales in 2011, when unemployment was still hovering around 9%.
As for the Wii, its sales trajectory was entirely normal for a Nintendo console, and there's no evidence that its success came at the expense of the 360 & PS3. And the DS would have destroyed the PSP regardless of the state of the economy, because A) it was a lot less expensive, and B) it's a Nintendo handheld, something that always does well. The PSP did well for itself, far better than any other non-Nintendo handheld, but there was no way it was going to be a close race between it and the DS.
Could the recession have had an impact? Possibly, but there's nothing about the trajectory of their sales curves that can't be just as easily explained by the same factors that affect every other console's sales. Even after adjusting for inflation, both systems were expensive compared to nearly every major console from generations prior. The Saturn was the only one on par with the PS3 (the 20GB PS3 was less expensive at launch than the Saturn was, but the 60GB SKU was more expensive). The 20GB 360 was the third most expensive console ever. Both systems remained more expensive throughout their lives than any other prior console at any given point in their lives. This was because of price cuts that were further between and proportionally smaller than price cuts older consoles got. The 360 as mentioned only experienced significant growth in the U.S. when it got a new model that resolved persistent and widespread hardware issues that tarnished the system's reputation. And both systems did their best when unemployment was at its worst. This even repeats in Europe, where the PS3 & 360 experienced steady growth throughout their early years on through to a 2011 peak. In Japan, both the PS3 and 360 peaked in 2009. Both regions also had tough economic times when we were (Japan less so than the others, but still).
TL;DR version: The sales trajectory of the PS3 & 360 can be fully explained by factors other than the economy, and external economic factors don't seem to correlate with anything in the sales data, not during last generation or any previous generation.