Hearts play Dundee United on Sunday, Kilmarnock on Boxing Day, Ross County before an Edinburgh derby with Hibernian leads into the mid-season break.
"Although we've maybe not had the season we were wanting, we're not a million miles away from everyone," McGlynn said.
"It just shows you with all the adversity, the doom and gloom and everything else, we're still not that far away from second and third place, which is probably realistically where we want to be challenging."
Hearts entered the weekend's fixtures in ninth position in the Clydesdale Bank Premier League, but five points behind fourth-placed Hibs, their rivals who have been praised for a strong season.
McGlynn is targeting a healthy festive points haul so Hearts can climb the table.
"We look to try to pick up as many points as we possibly can - 12 would be a great Christmas present and start to the new year," McGlynn said. "It can be done if you get a wee bit of a break along the way, because the games are going to be very tight.
"Every game is difficult in the SPL. There's very little between each team. Whatever you get you have to work extremely hard for it."
- Sports & Recreation
- Clydesdale Bank Premier League
- Dundee United