I do not believe in punishing people for having children, nor coercing, pressuring, or rewarding them for having fewer children- not only because I view it as governmental interference into the personal lives of its citizens, but also because it is unnecessary.
For decades, population control zealots thought that the only way to slow population growth was to do it forcibly or through massive campaigns; what we're slowly starting to realize is that if certain conditions are in place, men and women limit the number of children they have ALL ON THEIR OWN. You don't have to impose fines, at all; it simply happens. What are those conditions?
* Widely available contraceptive methods. If women have access to safe, legal reproductive healthcare- which includes short and long-term birth control, voluntary sterilization, and abortion- they tend to use it.
* Comprehensive sexual education. All the contraception in the world isn't going to help if men and women do not know how to use it.
* Economic opportunities. When men and women have opportunities for education and careers, guess what they do? That's right- they put off having children until they have attained those goals and have reached a level of financial security they deem appropriate for raising children. If, however, you live in a poor area and have no means of advancement, there really is no reason for you to not start a family right away.
* Women's equality. It should come as no surprise to us that in societies where women are seen primarily as mothers and homemakers and that is where they derive their worth, they will have more children. In societies where women's value is not tied into their ability to produce children, they are free to do as they choose- which still means having kids (most, but not all, women do want children eventually), but typically means postponing having them, and only having the number they really want, not continuously bearing them because they feel they have to. Similarly, in some societies, boys are prized over girls, which often leads women to have many more children. In some countries, like India and China, this leads to sex-selective abortion, but in others where girls are less of a financial burden or sex-selective abortion technology is not available, they simply have far, far more daughters than they would otherwise, all in the attempts to have one or more sons.
* Secularism. Religious communities often believe our purpose is to "be fruitful and multiply" (typically combining this sentiment with one that views women as solely mothers and homemakers, as demonstrated above). And, of course, some religions do prohibit all use of contraception, like Catholics. But even for those which do allow birth control in limited situations, they may still engender a sex-negative environment, which can depress usage of birth control (as I describe below). Societies need a certain degree of secularism, usually, to depress the rate of reproduction.
* Sex-positivity. If certain forms of sex, like non-marital or pre-martial sex, are stigmatized within a society, those who practice it are less likely to use protection. Teenagers who know their parents will be angry and punish them for having sex often will not risk having condoms or birth control pills found out- that evidence is incriminating, after all. Small-town teenagers may not want to buy condoms at a local store where others may see them doing so and spread the information. So long as certain forms of sex are judged negatively in our society, it will be less feasible to use birth control, and that will lead to more unplanned pregnancy.
When all of these things are working in conjunction, most women voluntarily choose to limit the size of their families. You don't have to forcibly sterilize people, and you don't have to levy fines.
Would a campaign like Singapore's affect my decision to have as many kids as I wanted? Probably. If I was in the financial situation to absorb the fines, and I wanted more than two children (which I don't), I probably would have the kids anyways. If I couldn't really afford it, I would probably be forced to limit the size of my family against my will.