Probably not very much, even though critics have blamed expansionary monetary policy in the past for exacerbating both the dot.com bubble of the late 1990s and the more recent and more destructive housing bubble whose collapse (and related derivatives markets) precipitated the Great Recession. On April 30 in Washingon, Alice Rivlin declared that everybody at the Fed knew there was a stock market bubble in the late 90s, but had no idea what to do about it, fearing that raising interest rates would just tank the whole economy. At the same function, Donald Kohn said that people at the Fed were unsure if there was a housing bubble or not in 2005, and while suspicious that housing prices were indeed too high, thought that they would be able to come down without damaging the whole economy. Minutes from a crucial meeting on this in June, 2005 can be found at http://www.federalreserve.gov/monetarypolicy/files/FOMC20050630meeting.pdf .
Presentations were given at that meeting taking different positions and with the commentaries all over the place. Janet Yellen, leading candidate to succeed Bernanke as Fed Chair, comes across as possibly the best informed and most careful of all the commentators in the room that day. Looking particularly silly was then St. Louis Fed President William Poole, who argued essentially that bubbles are impossible because people will be rationally optimizing across time periods. Someone taking the possibility of housing bubbles seriously, if not too worked up about the possibility, was then Vice Chair, Timothy Geithner. Curiously, over a year later in September, 2006, after the housing bubble peaked and he had become President of the New York Fed, Geithner became much more concerned about the general state of financial markets, his position being described by Kohn on April 30 as "banging the gong" about systemic risk, although Kohn said that by then "it was too late to do anything about structural changes." Geithner's speech is at http://www.newyorkfed.org/newsevents/speeches/2006/gei060914.html .
While much of the speech was pollyannish, and he made no specific reference to the decline of housing prices or to the CDOs et al based on overrated and failing mortgages, the flavor of much of it can be seen in the following on risk management from it:
"Understanding and evaluating 'tail events' - low probability, high severity instances of stress - is a principal, and extraordinarily difficult, aspect of risk management. These challenges have likely increased with the complexity of financial instruments, the opacity of some counterparts, the rapidity with which large positions can change, and the potential feedback effects associated with leveraged positions."
Anyway, the issue is back and some argue that the latest reports of rising housing prices in many markets, over 12% nationally according to Case-Shiller index for the last year, and over 20% in Phoenix, along with the reports of the reappearance of flippers in some markets, suggest that the ongoing QE policies by the Fed are reigniting the housing bubble, and that therefore these should be reined in sooner rather than later. However, most observers agree with Rivlin that interest rate policies should not be driven by fear of bubbles, but that other regulatory instruments should be used, such as minimum downpayments and the forbidding of interest-only and other unorthodox mortgages. Indeed, a reason to believe what is going on now is not a bubble (at least not yet) is precisely that financial institutions have put in place much tighter restrictions on mortgages that are arguably keeping people from buying homes who ought to be able to do so.
Regarding the flipper situation, it would appear that so far most of these people are dealing in foreclosure auctions, which are quite a different matter from the sort of thing that was going on in the later stages of the housing bubble that peaked in 2006. Indeed, it has been reported that these agents often are fixing up the places that they buy to flip, thereby upgrading damaged properties and thereby improving the fundamental condition of the housing market, rather than generating some new bubble, even in Phoenix. A report on this is at http://realestate.msn.com/article.aspix?cp-documentid=23091817 .