Hearts relinquished their hold on the William Hill Scottish Cup, won in May by McGlynn's predecessor Paulo Sergio, at the first hurdle last Sunday, with a 1-0 Edinburgh derby loss at Hibernian.
Sergio and numerous players departed following the Hampden success as a result of cost-cutting measures and there is a hint of stability at Tynecastle following this week's announcements that a winding-up order has been avoided and an agreement has been reached over the repayment of another tax demand.
Amid the myriad of financial problems, Hearts have toiled on the field and sit ninth in the Clydesdale Bank Premier League ahead of Saturday's match with Aberdeen.
McGlynn said: "I've got a two-year contract. I intend to see that out.
"No one puts me under any more pressure than myself. I don't like losing, I don't like the situation.
"It's fire-fighting every single day. You just dust yourself down and get on with it.
"The biggest fight is for Hearts to survive. That is the priority."