What would be the consequences of this corporate tax policy?

Without having thought through the idea thoroughly, I'm curious for feedback:

The US is the most powerful consumer nation on the planet with 300 million people and an enormous trade deficit. No large corporation would forgo our market because if they did they would be out-competed by companies that do business here. Given that, what if we instituted a policy that said every corporation that does business in the United States must pay the US corporate tax rate? Setting that rate is a different debate, I'm just talking about closing a loophole, not the appropriate tax rate. Taxes paid in foreign countries could be deducted so corporations aren't paying double tax, it just means they pay at minimum the US tax rate, even if some of that rate is paid to other countries in which they do business.

What this prevents is corporations putting all their earnings on the books of tax shelter subsidiaries in Bermuda and other places like that. GE not only paid zero taxes, they actually got a tax subsidy last year in spite of making 15 billion. They are not alone, these types of numbers are common among large corporations. If we end the policy of keeping money off-shore in tax shelters, we would recover many billions in corporate taxes.

I think this policy would achieve that without the negative effects that are commonly feared, which are that companies will shift manufacturing (and jobs) off-shore. Here, as long as companies want to sell in US markets (and they do), it doesn't matter where they are located, they must pay US tax rates.

We may want to exempt small businesses so they can enter the US market more easily or we may not so that the ones who are here can be protected from foreign small business competitors operating in tax shelter nations. I could see going either ways on that.

What do you think would be the response? What problems do you foresee? What solutions might there be for such problems to still achieve the goal?

Thanks.