Some people still refuse to pay. Often, they end up in court. Sometimes, they even win their cases. The problem is this: even if some people win their cases, the average result is that a tax protestor ends up paying the taxes owed. Plus fines. Plus, his lawyers will have some extra income from defending him, and they'll pay taxes on that.
In other words, it's not practically effective. But let's suspend our disbelief for a bit, and ask what would happen if people started winning these cases — if the jury agreed that the government had accidentally omitted a crucial clause from a critical sentence, and nobody legally owed income taxes. What would happen is that Congress would hastily meet, add back the offending clause, and be done with it. After all, they passed the Sixteenth Amendment specifically to authorize income taxes. If they hadn't meant to make income taxes the law, they wouldn't have rewritten the constitution.
If Congress acts like paying taxes is the law, and taxpayers act like it's the law, and only a few law-parsers say otherwise — the law will change, not the country. If you want to pay lower taxes, there are three things you can do that will get you good results: you can structure your spending and saving to take advantage of tax breaks; you can get involved in politics and try to make the government more responsible and less spendthrift; or you can make less money. If none of that sounds appetizing, you may just have to move.