One addition to Su.Ki.'s answer.

I have an impression that this thing which "someone has said previously" can be imaginable:)
When I read this 'do', I don't necessary see any "don't" above.... But definitely, a contradiction/an argument of some kind is implied.

Though Su.Ki. is a native speaker and I'm not.  So, if i'm wrong here....

thx for ur help, u explained a lot and now, I understand more 

cherry,
1. Do
"I do deserve you" means more or less the same as "I deserve you"... or even "I deserve you".

'Do' is added to stress this fact... Or rather this way:
You are considering two mutually excludind options: "do deserve" and "do not deserve".
Adding 'do', you mean, that it is really and exaclty "do" and not the opposite!


2. deserve
see dictionary
Here it means: "good enough for you".
Such phrase might arise in the context of romantic relations or marriage, for example.
It can mean:

a1: - I'm good (or bad, or rich, or clever, or beatiful, or caring or) enough person, so it is natural that I have met such a good (bad....) girl as you. That God send you to me, if you like)
a2: - I have done a lot of good things, and you are the avard I deserve.

b1: - I'm good enough to fit such a bright person as you.
b2: - I've done something to prove that I'm good enough for you:) I have demonstrated that I'm faithful and caring.

Most likely it is B1.

Initially this word came from "to serve". Imagine, you are a king, and you command me to conquer Cambodia (I am at your service then). I go and conquer Cambodia and I do it even sooner than ou could expect:) Now I definitely <em>deserve</em> an award.
So it could mean "to earn an award".

But now it in most cases (except for those on actual <em>service</em>) is just "good enough for". Still it is often said in context of some achievement:
a good scientific article deserves a publication in a prestigeous journal.

And just to confirm...

Yes, you are right. This is a positive statement. The dictionary that told you it is negative is wrong.

ok, I got it ！thx a lot ！