America's an interesting case of political development I often find myself thinking in horticultural metaphors after reading deeply into this for a few years (Hartz was the turning point for me).
Essentially, you have to look at North America through the lens of its European ancestry (so I often think of taking a part of a tree, for example, and planting it somewhere new). There were a few feudal regions (Quebec and the South) but most of the rest of the United states was dominated by a classically liberal political philosophy. In Canada, and especially after the revolutionary War, you had that of course but also a persistent conservative Toryism the Americans ended up losing the final vestiges of with the death of the Whig party. Socialism crested a bit maybe in the 1800s but then died a death that has left it relegated to the bucket of alien concepts shunned as "un-American".
So over the course of America's development you have this shedding of competing philosophies: tory conservatism dies, the feudal south becomes integrated into the Union after the war and that falls by the wayside, socialism is weak and then excommunicated.
What you're left with is - on the whole - a purified liberal starting point for most of modern American politics. What's interesting is that the divide between the right and left in America is a debate between different conceptions of liberalism: with one tending towards the libertarian/individual axis and the other towards the Hamiltonian axis of stronger federal influence. But because all America knows right now is some form of liberalism, they need to redefine liberalism to be a subset of their polity rather than describing their entire polity (which, from an objective outsider's perspective, "liberalism" certainly does).
And this, my Swedish friend in the OP, is why "liberal" is seen differently for you (for me in Canada too) as we have more diverse political spectrums that structure our political culture: socialists actually exist in our countries and can be elected! Yes, imagine a party of Bernie Sanders types instead of just one lonesome voice in the wilderness!
We have traditions of conservatism that have long since been killed in America. So for us, the word "liberal" does have a different connotation.
Now, I've come to realize that in fact - what I'm used to doesn't really matter in America. Whatever its usage elsewhere, we know exactly the cartoon character people like Rush are sketching when they use the word.
And since it has meaning and relevance to millions of people in that sense, well we just kind of have to accept that as the way things are there.