Sorry, I don't follow this. The difficulty of an action doesn't correlate with its popularity. In fact, the most difficult actions are often the most widely acclaimed.
In a historic context, with the benefit of hindsight, this is true.. In the short term, however, hard but right works are usually incredibly unpopular.
An example would be the treatment of real estate in Australia.
Howard & Costello helped fuel the last 10-15 years of frenzied speculation in real estate with their tax changes (in particular, the halving of capital gains tax). This was immensely popular, since it allowed people to facilitate "equity mate" and use their unearned wealth to go out and buy cars, jetskis, and overseas holidays, while a) digging themselves deeper and deeper into debt and b) hanging a giant albatross around the neck of Australia's economy.
The "right" thing to do would be to make real estate as cheap as possible, and use the tax system to punish rent-seekers and others in search of unproductive and unearned wealth (eg: by getting rid of negative gearing, and having punishingly high CGT for short-term holders). However, it would be deeply, deeply unpopular since a) a whole bunch of people who currently think themselves "rich" would find they are not, and b) they might actually have to go out and do some real, productive work.
Now, would doing this be popular eventually, over the long run, once even people on minimum wage could afford to buy their own home ? Sure. But during the transition period someone like Tony Abbot would be spreading as much fear, uncertainty and doubt as was humanly possible, accusations of wealth destruction would be flying left, right and centre, and people like you would be cheering him along.
If a thing is unpopular but needed for good government, then it means that the thing hasn't been presented well. People aren't stupid; if they know the facts, then they will follow the logic.
Well "knowing the facts" is one of the problems, innit ? After all, just look at how many people think the carbon tax is why their electricity bills have gone up 50% (or whatever it is).
Further, it's quite possible for a "right" thing to be unpopular in the short term, yet considered completely differently in the long term. The ending of slavery in the US South, for example.
My point about popularity is that good government, like wise leadership or a good safety record or whatever will bring about its own popularity. That's what democracy boils down to in respect to government, after all. In aviation terms an airline can be as cheap or as luxurious as it wants, but if its planes crash too often, it won't have too many passengers choosing it, thank you Rain Man.
When people choose the wrong airline it only affects them. When people chose the wrong Government, it affects everyone. Treating refugees like lepers and homosexuals like second-class citizens isn't "right", but it sure does seem to be "popular". Policy shouldn't be decided by popularity.