The Minstermen are seven points adrift of safety with nine games to play, six of which are against teams currently sitting in the top eight.
Despite that, Easter does offer a glimmer of hope with today seeing 16th-placed Crawley Town head to Bootham Crescent before York travel to faltering Plymouth Argyle on Monday.
Nearest rivals Stevenage, meanwhile, travel to second- placed Oxford today and are then without a fixture due to the scheduled home clash with Yeovil Town having been postponed because of international call-ups.
That leaves York with a chance of making inroads into the points advantage currently enjoyed by third-bottom Stevenage, who yesterday appointed Glenn Roeder as director of football.
McNamara, for one, remains adamant that York can get out of trouble.
“I still believe,” said the Scot. “I am not saying that for the sake of saying it. I do believe we have enough to stay in this league. I totally believe that.
“I work with them every day. Some might see them just on a Saturday and see fear. But, starting with Crawley, three of the next four fixtures are at home. If we win our home games, that will keep us in the division.”
Bradley Fewster is struggling with a back injury that is related to an earlier hamstring problem, the loanee rated as hugely doubtful for the visit of Crawley.
Michael Coulson, though, is in the squad and could feature.
Last six games: York City LLLLDL, Crawley Town DLWWDW.
Referee: P Gibbs (West Midlands).
Last time: York City 1 Crawley Town 1; April 5, 2011; Conference.