I think it's possible, but you have to put aside your preconceptions of whatever it is and approach it with a fresh and open mind. Alright, so at first glance it isn't very appealing, but have you really looked at all of it? All you really need to do is find one thing about it that you like, and focus on getting as much enjoyment out of that as you can. Once you've found something you like about it, it's not so difficult to isolate something else, and then something else, and so on. Before you know it, it's not quite so tedious anymore.
It's also a lot easier if you have someone to share it with. You can talk to them about it and develop your interest in it with them, making it easier to sustain an interest in it. It doesn't even have to be someone you're close to, just someone you can stand to talk to. I think this is especially true of jobs where the work can be especially monotonous sometimes, and the environment in which you're doing the thing can make it very enjoyable. As an example, I absolutely loathed working in my local Tesco Express, as I was standing on tills from 6am to around 2pm. But I got to know a lot of regular customers and it made the job that much more bearable...I wouldn't say I ever had a passion for it, but it's just an example of how environment can make things tolerable, even if you have no interest in the area.
Maybe you're setting your sights too high, too. If it's something you don't enjoy, start with just tolerating it and taking pleasure in the small moments of satisfaction you get from doing it before you start trying to actively enjoy it - in the long run satisfaction is far easier to maintain and cultivate than passion, because it's on a smaller scale and isn't wholly dependant on your mood. Even the things I'm most passionate about I get no pleasure from if I'm not in the mood for them, but satisfaction is easy to achieve if I set realistic goals and targets for myself.
Most areas are pretty broad, and if you want to cultivate and maintain passion in it, try narrowing it down first and finding the things you like about it. Maybe it doesn't work for everything, but I'd say it depends on your mindset...and yeah, some people have the ability to adopt that mindset, and others don't. Maybe start by asking yourself why you want to bother in the first place if it's that unappealing. xD