Multiple studies have now linked chronic use of these painkillers with an increased risk of heart attack and stroke. They mechanisms appear to be mediated through the inhibition of an enzyme known as Cox 2. There have been a couple of mechanisms investigated in animal studies. First, NSAIDs have been shown to inhibit the production of a molecule called prostacyclin that relaxes blood vessels and “unglues” platelets. Second, they have been shown to inhibit the production of nitric oxide (which cox 2 also regulates to some degree).
To hear a longer discuss surounding NSAIDS and heart attack risk, as well as the relevance of curcumin in pain-relief make sure to check out JRE#773 or, more recently, Tim Ferriss Show #237 where both topics are discussed.