The William Hill Scottish Cup final win over Hibs aside, Hearts endured a torrid 2012 and remain mired in financial difficulty. They lost December's most recent Edinburgh derby, in the Scottish Cup fourth round, as a 12-match unbeaten run came to an end.
Hibs have been praised for challenging towards the top of the table after battling relegation in recent seasons, but McGlynn is optimistic his side, who have a game in hand, could soon overhaul their capital rivals.
"It's up to us to rise to the challenge," McGlynn said. "If we can win that game tonight, we would be three points behind Hibs with a game in hand.
"Considering the situation we've come through, that would be a reasonably good position to be in, sitting in a comfortable position for the second half of the season."
Hearts will be without Ryan McGowan after the club accepted a bid from China's Shandong Luneng, believed to be in the region of £400,000, for the 23-year-old Australia international, whose contract is due to expire at the end of the season.
"It's disappointing to lose him but it's the state of affairs," McGlynn said.
"If good offers come in, in the financial situation we find ourselves in, we need to accept them."
McGowan was seen at Hearts' training base in west Edinburgh on the eve of the match saying his goodbyes.