Should the government focus on ensuring businesses pay their 'fair share' of federal taxes?

I have seen a lot of discussion on personal income tax and raising (or lowering) it for the highest personal income levels. Wouldn’t it be more cost effective (generate more income versus the amount of work) to first ensure large companies who make large profits are paying their fair share of federal taxes?

Reading this article is what prompted this question. In particular this quote, “This comes amid disclosures of low tax payments by some of the nation’s biggest companies, including General Electric Co., which made $14.2 billion in worldwide profits last year, but paid no U.S. corporate taxes in 2010.”