New Englander here.
What in the world is a "New England accent?"
Do you mean Boston? New Hampshire? Wood Chuck? Whatever the hell is going on in Maine? (I didn't know anybody lived there to have an accent.)
It does not. It's more of a mix of Midwestern, border mexican, valley, and standard Texan. I loved how many of the Indian tech-workers that moved to Austin in the early 2000s quickly developed a habit of using y'all...and a breakfast taco addiction.
I live in Jackson, Wyoming (right on the border with Idaho for 8 months out of the year. I travel most of Idaho, Montana, and Wyoming, and I do not detect a difference in accent between there and most of the Midwest.