Nobody's talking about "taxing other countries".
US law says that, if you're a US citizen, you're liable for US taxes. Doesn't matter where you live or where your money comes from. However, it also recognises that it's not nice to subject citizens residing overseas to double taxation--so if you live in $country and pay $country's taxes on your income there, the US will often accept this as having fulfilled your obligation. But if you've income that you're not paying taxes on, anywhere, and the IRS finds out, they will come calling.
What Obama is apparently intending is to extend this philosophy to US corporations, which currently enjoy a much better deal than you or I. They pay US taxes on profits reported in the US. They don't pay US taxes on profits reported in other countries--and here comes the important part--even if they report those profits in $nation, which happens to have negligible or even zero corporate taxes. Whereas, if I move to $nation and they don't make me pay income tax there, then I get to pay it to the US.
So corporations currently get a huge overseas tax dodge that you and I don't. Quoth TFS,
In the future, the budget proposes that U.S. companies pay a 19 percent tax on all of their foreign earnings as they are earned, while a tax credit would be issued for foreign taxes paid, the official said.
So in other words, US corporations making money overseas would be subject to taxes on it in a manner very much like how US citizens are already subject to their overseas earnings, and with same proviso that they won't be doubly taxed.
Okay, go ahead and explain how this is "retarded" or unfair. Seems pretty smart and fair to me.