IMO Microsoft shouldn't comply, and the US goverment should back them.
To be entirely honest the US economy isn't in great shape and we've spent billions bailing Europe out of debt when we really couldn't afford it. Microsoft is a US company and it's revenues and trade results in taxes and tariffs going into US coffers. Something as prolific as web browsing software and the amount of money/power that gives Microsoft can translate into a lot of cash for the US if our goverment is smart about it for once.
The EU's perspective in cases like this (which involve a lot of things) is that they don't want to be beholden practically or financially to foreign/US technology. Not to mention being able to produce and circulate more euro-centric browsers allows them to more easily control information through software created in their back yard.
On one hand I can understand the EU striving for financial and technological independance, which is part of what the EU and it's trade policies were about. On the other I feel their big attempt failed, and the US which was already a wreck had to step in and help the guys who sought to replace us, to keep the market open if nothing else. Under the circumstances I pretty much want to see Europe more beholden to the US.
This is a complicated matter that could be discussed heavily here, especially with international Escapists from Europe, so I'm not going to get into it at the moment, especially seeing as what I'm saying isn't very nice overall, and the discussion could get nasty. Right now I am very believe in a "US first" policy with all of our problems and doing what we need to for ourselves. We helped bail our Europe, but I think it's stupid to be entirely philanthropic about this given our problems. As I see things the activities of US based companies directly impact the bottom line for the US. Microsoft itself, as large as it is, might be a drop in the bucket, but those drops add up if we pretty much stick to what's going to give us much needed money, power, and control when those things are slipping.
Not to mention that there is something of a humanitarian interest here. While anti-trust is invoked and browsers like "Firefox" and "Chrome" are mentioned, I've read a lot about European censorship, suerveillance, and free speech issues, many conducted under the arguements of "cultural protection from foreign ideas". I believe France in paticular was kind of vocal about US media eroding the French identity. Cooperate too much and it won't be Europeans going to other, untouched, browsers, but probably being gradually sheparded into ones that can be better controlled. It's funny because I think half the problem is that Microsoft for all of it's exploitation prevents goverments from doing too much of their own, at least not on the level that they would like to.
I doubt it will happen, especially if Obama hits term 2 (he's not a big believer in big business as a foundation for the country) but this is the kind of case where I think the interests of the US and a company coincide... at least to an extent. With Europe in the condition it's in right now and it's dependancy on bailout money, now is the time to push US business interests in the region.