The Canaries are currently on a run of eight games without a win in all competitions and slumped to a 3-0 defeat at Fulham in their FA Cup third-round replay on Tuesday night.
A number of the club's supporters have started calling on the board to act, with Malky Mackay's name sang by the travelling contingent at Craven Cottage.
The former Cardiff boss was a fan favourite during his time as a player at Carrow Road but for now Hughton's job is safe, although McNally insists he will do anything he deems necessary to keep the club in the top flight.
"He [Hughton] is preparing the team for Saturday's game," McNally told BBC Radio Norfolk.
"The brief to Chris was to keep us out of the bottom three, we are not in the bottom three and it is to keep us out of the bottom three so that is what we have to do. We would not contemplate relegation at our football club.
"In a sporting sense it [relegation] is worse than death."
Norwich are currently 15th in the standings on 20 points, two clear of the bottom three.
"We are absolutely focused on ensuring that this great football club stays in the PL, too many people have worked too hard and for so long to put the club in the PL so we would do everything in our power to ensure that it not only stays in the league but thrives in the league," added McNally.
"The brief for Chris when we were in the bottom three earlier in the season was to get us out and keep us out of the bottom three and move us up the table.
"There is no change there. If you don't produce the results then ultimately that is how you will be measured."
Hughton is likely to venture into the transfer market in January and has already recruited Newcastle midfielder Jonas Gutierrez on loan for the remainder of the campaign.
The 55-year-old has been in charge at Carrow Road since he was appointed as successor to Paul Lambert in June 2012 and led the Canaries to an 11th-placed finish last season, their highest final league position since 1993.