I am a tourist working remotely for my own company while in the US.

Technically you need a visa. Practically as long as invoices are coming from your own country and the money is going to your own country, nobody will care (or even notice).

Unless of course you make posts like this one in a public forum under a name everyone knows you under. But I am counting on inefficiencies and the good will of fellow hackernewsers. (you'd need to actively get reported for anything to happen)

PS: having an actual tourist/business visitor's visa rather than just the visa waiver (esta) makes things easier and border crossings go much smoother

Swizec's answer is good, you technically need a visa. If you can afford to be kicked out of the country and not be allowed back in for a long time (10 years in the US), then it might be worth the risk of not getting the visa. But, if you can't risk being banned, or even if you just like to obey the law, you should get the visa, especially if it's easy... which it is for a lot of countries.