No, I think the ball is clearly in the Republicans corner concerning tax policy. The goal of Democrats is to have government control the spending, not private entities.
First off, that money would benefit America greatly IF it was used domestically to create more facilities, hire more labor, or encourage R&D spending by acquisitions or investment in US companies, or organic R&D spending, etc... etc... so I would propose making the cash import taxable, but giving a write off for spending it domestically, bolstering domestic investment. Paying dividiends or share buyback not included, since the majority of these companies shares are foreign owned.
As far as Apple specifically is concerned, they have had their fare share of bad press on these issues. They do have a valid argument as to why they operate this way: local competition.
When a company in Japan sells goods in Japan, it pays Japanese sales tax. It then pays Japanese income tax on its profits. When Apple does it, it pays Japanese Sales Tax, Japanese income tax (for that entity ( the local Apple subsidiary)), and then American income tax on top of that, three taxes. It minimizes this third tax by diverting the income to Ireland and holding it there. They and everyone else knows that this third tax creates an unfair playing field against global or international companies because domestic ones don't have to pay that transfer costs. If you feel that this tax is fair, every company will eventually build it's headquarters in China, since long term that's where the majority of their income will be generated.
Stiglitz is wrong here.