But there's also a long-term component: this is something that's been developing over decades. If conservatism is basically defense of the status quo, you'd expect it to have the central institutions of society on its side. Historically, that's usually been the case. But in the 1960s-70s, prevailing political views at universities (especially elite ones) went from being mostly moderate or slightly conservative to being overwhelmingly on the left. A similar development happened with newspapers and magazines, especially "quality" ones, although it didn't go as far. That's one reason that conservatives feel embattled--they have a sense a sense that an important part of the "establishment" is against them. Universities are especially important, since young adulthood is when many people start getting interested in politics.
The limitation of this explanation it doesn't explain why contemporary American conservatism is particularly ideological by international standards. Although I don't have good data, I think the shift of higher education to the left is a widespread phenomenon, and in many countries universities have traditionally been centers of radical politics. I think that the answer may be that, compared to other nations, Americans are conservative on a lot of "moral" beliefs. For example, although the United States has a high divorce rate, Americans are less likely to approve of divorce than people in almost all other affluent nations (which reminds me that I should have a post on that subject). The social changes of the 1960s and 1970s haven't been rolled back, and in some ways have continued to go on with no signs of stopping: for example, growing acceptance of gays and lesbians. I think this is why American conservatives continue to feel embattled even though the last 30 years have been a fairly conservative period in other ways.
Being embattled means that people are going to stick together, and work harder to justify their views. The left was traditionally sustained by a sense that elites were against them, but the common people were (at least potentially) on their side; now that feeling is also found on the right.