Outside of the US frame of reference, Obama is very much a conservative, and Democrat policies would happily work in right-wing parties. Obama is definitely not a moderate when viewed in a global sense.
Do you really imagine that someone trying to set up mandatory EU-wide health insurance in the EU would be considered "conservative" in Europe? Notwithstanding that "conservative" means very different things, depending on which part of Europe you are in.
The idea that there is an objective left-right scale, and that the US is skewed far right compared to the rest of the world is a myth.
Personally, I tend to the definitions: left - pretends to be caring; right - pretends to be competent.
Nice reframing. Yes, if said person was taking away the socialised healthcare that's already in place across much of Europe and replacing it with the much more business-friendly version promoted by the Democrats, they absolutely, positively would be seen as being what we term 'conservative' (or right wing anologue - in Russia, they are reversed, apparently).
I doubt that the Democratic political culture would be considered conservative anywhere in Western Europe: they do the normal leftist thing of trying to build power through coalitions of victim groups, trying to raise taxes on the rich, and so forth.
I can assure you that in the UK, replacing the NHS with an EU-wide health care system would not be seen as conservative, whether you see it as "pro business" or not.
What policies of the Democratic party do you think would be considered conservative?