Does Denmark have a federal deficit?

I recently saw an episode on Oprah showing how people live around the world. Denmark was the first featured, they explained that the country has socialized medicine; people rarely work past 4:00 pm; up to 4 years of federal help if you lose your job; and people get paid while going to college, and the tuition is free.

So, I wondered if this has been working when looking at practical concerns like federal deficit, economy, standard of living, etc., and for how long it has been sustainable? The country seemed so civilized (a reputation they have in general in my mind).

Denmark seemed like a country Gene Roddenberry would invent, except everyone is blond.