A run of just one victory from their last six Premier League outings has seen the Canaries slip to 14th in the table, just four points above the drop zone.
A victory over the Swans would go a long way to securing Norwich's status as a top-flight club for another campaign and with that in mind, Scotland international Snodgrass has called upon the supporters to get behind the players once again.
"Everybody needs to be pulling now. We need a very busy, loud Carrow Road to edge us across that white line and try to get three points against Swansea," he told the Eastern Daily Press.
"The way the Everton game was, they were willing us to try to get the ball in the back of the net and we need that ready for a big push now."
Norwich have lost just three league matches at home all season.