Yes. This is the way that the public choice theory of government explains the success of special interest groups - an issue may have a majority of voters against it but if a small minority care enough about it to change their votes over it (whereas the majority who disagree are unlikely to do so because they don’t care enough about it), it can make sense for politicians to offer strong support to unpopular special interest positions.

I suppose there’s a sort of deranged case where every issue a politician supports falls into this category though it’s probably not the norm.