In the Marvel Universe continuity 616, the canon universe of the Marvel Comics, no, the origin story of the Avengers does not have the city spanning effect that the trailers for the movie are currently showing. The origin of the Avengers did have Loki as the primary instigator, but there was no city destroying event as the backdrop.
There are echoes of the Ultimates continuity (Marvel Earth Timeline #1610) where Nick Fury is a Black man, and there were no other superheroes until the late 20th Century, with the exception of Captain America, who was still created during World War II.
The closest analog I can find is an animated television series, The Avengers: Earth's Mightiest Heroes, which premiered on October 20, 2010. The animated series starts with a storyline similar to the movie except the enemy is Kang the Conquerer, a time-traveler who comes to the past in order to prevent events which lead to the destruction of his future. The first two episodes show a war across the city of New York very similar to the trailers for the new movie coming out.
I am certain this is not an accident as they wanted an event to be large enough to challenge the physical capabilities of the three most powerful Avengers, Thor, Hulk and Iron Man, as well as an event filled with military operations which allow Captain America, Black Widow, Hawkeye, Nick Fury and the organization of SHIELD to be involved.