Mitt Romney chose to wrap up his primary win last night with an extensive discourse on the evils of Europe, and of Barack Obama's plans to turn the United States into a European-style socialist dystopia. Since American liberals are generally more cosmpolitan and less nationalistic than American conservatives, the tendency is for liberals to explicitly point to Europe as an example of some things they want to do and for conservatives to explicitly point to Europe as a cautionary tale, but it's worth noting that Europe is quite conservative in many ways. For example, the American right has lately fallen out of love with both J.M. Keynes' fiscal stimulus ideas and Milton Friedman's monetary stimulus ideas. Tussle between these two has dominated practical policymaking for decades in the United States, but if conservatives were to cast their eyes toward Europe they'll find a continent where these ideas about demand-side management get short shrift. The kind of "internal devaluation" that European officials have been touting in Estonia and Ireland, and pushing on Italy and Spain, is very much in keeping with state of the art thinking on the American right.
Conservatives will also find that Europe is much less open to immigration than the United States, that Europe generally has much lighter taxation of investment income, that few European countries uphold American-style strong separation of church and state, that European countries generally afford accused criminals fewer procedural rights, and that Europe has much less in the way of product liability and class action lawsuits. What's more, though there are a few exceptions (Sweden comes to mind), Europe as a whole is more conservative in its gender norms in many ways. Women's workforce participation rates are lower, fewer children are born to single parents, and there are many more legal restrictions on abortion.
So beyond the point that there's a great deal of diversity in public policy and social conditions within the European continent, it's really not clear to me whether it's liberals or conservatives who actually want to make America more "like Europe." The image most people have in their heads of Europe is dominated by non-policy aspects of the landscape—Europe has more old building, older urban forms, and it's more crowded—and the proclivity to praise or criticize Europe seems to me to be explained entirely by the nationalism/cosmpolitanism gap rather than any objective analysis of the European policy environment.