Having seemingly swept all before them this season, City were held to a goalless draw at West Brom on Boxing Day, with the red half of the city pulling level on points courtesy of a 5-0 win over Wigan.
And England stopper Hart has acknowledged the heat being generated by United, but is in no doubt he and his team-mates are up for the fight.
He told a number of national newspapers: "Of course we feel the pressure. You have to earn the title and it's hard work.
"We're the team to beat and we're enjoying that but it's not always going to be as easy as we've sometimes made it look in the past.
"Of course it's disappointing not to have won again but West Brom set out for a point and they got it. We need to be winning these games but we haven't and we move on."