what does 'nudge' mean?
I know that it literally means 'to push in a gentle way'. What I'm asking is that, what kind of other meaning, e.g. as in a metaphor, can it carry?

I believe I heard something like ' The latest budget nudged half a trillion deficit' . So why use 'nudge' in this case? Or I could be wrong, it might be a different word that I miss understood.

Question

what does 'nudge' mean?
I know that it literally means 'to push in a gentle way'. What I'm asking is that, what kind of other meaning, e.g. as in a metaphor, can it carry?

I believe I heard something like ' The latest budget nudged half a trillion deficit' . So why use 'nudge' in this case? Or I could be wrong, it might be a different word that I miss understood.

Answer

So in this instance nudge still carries the same meaning but it is a metaphor as you guessed.
In your example a budget obviously can not physically nudge anything, but it can help create some non-physical economic change or boost.  
The meaning is still the same though 'to push in a gentle way'.  The budget is 'pushing' the economy forward/up.

Answer

Before you can gently push something, you have to approach or get near it. Therefore, in your context, I think "nudged" is used to mean "approached" or "touched."

I just checked the Free Dictionary. One of the definitions for "nudge" on that site is, "To come close to; near."
http://www.thefreedictionary.com/nudge

Answer

"Nudge" can be without an object, and mean to move slightly in a certain direction, or come close to something by small degrees (eg. nudge forward, nudge closer, nudge by).  In your example, "nudged" means "came very close to".