I believe you're referring to a trochaic rhythm.

This isn't stream of consciousness as some have suggested because it makes narrative sense, even if it isn't telling a chronological narrative. Stream of consciousness is more impressionistic.

the rhythm is what is giving it that "word vomit" effect, and we call this rhythm Trochaic. It's sort of the opposite of iambic. The line begins stressed, and regresses to unstressed.

With your face and your beautiful eyes
And the conversation with the little white lies
And the faded picture of a beautiful night
You carry me from your car up the stairs
And I broke down cryin' was it worth this mess?
After everything and that little black dress
After everything, I must confess I need you

the chorus plus this verse yields essentially a 12 line trochaic sonnet.