Probably you can find the negative meaning of 一条狗 from 周星驰 (Stephen Chow)'s movie 《大话西游之仙履奇缘》：
That person looks strange, he looks like a dog.
You see that person? He looks like a dog.
"一条狗" here indicates they thought that person is a "poor guy" rather than "a dog".
But don't use this if you're not familiar with the people you're talking to!
In most cases, we just make fun of our friend or our self that we use "一条狗" to refer to some difficult situation, and have no negative connotation at all, for example:
I'm working at Shanghai, and I get paid 20,000 yuan each month, and live here is not better than a dog's life.