Should there be any legal limits on the size of business or organizations in the U.S.?
Interesting question. According to U.S. law under the Sherman Anti-Trust Act, a company that exceeds 75% of total market share for their product line has monopoly power over that product and is subject to being challenged by anti-trust laws for potential separation of the organization into different separate organizations. A company that maintains between 50%-75% market share is considered inconclusive and anti-trust actions, if any, will be taken on a case-by-case basis. By the same token, when organizations agree to collude over products or territories so they do not compete with each other will be prosecuted as long as they have more than 10% market share between them. So, from a legal perspective, a business is considered too big when it starts to exert monopoly power.
Economically, this makes sense as well, and could be used as a guideline for an organization being too big. Whether a natural monopoly or not, monopolies (and, for that matter, oligopolies) have a negative influence on global economies. They cause decreases in innovation and increased costs (for more information on monopolies and oligopolies, please go here: http://www.investopedia.com/university/economics/economics6.asp#axzz2Cc2bhF97
As for the pure size an organization getting too big, there is a lot of controversy that surrounds some of the largest multinational corporations, but the cause of the controversy often comes not purely from their size, but from their actions; political coercion, social manipulation, and things of that nature - things that not all big companies participate in, and which not all offenders are necessarily very large.
Theoretically, it is also possible for a single company to become too large without actually being a monopoly when it begins to influence a nation's production possibilities curve to include allocations of the factors of production that are less efficient than those would be possible if the company was smaller. In other words, a company could be considered too big if it is consuming so many resources per unit of output that total national resource efficiency decreases as it consumes resources that could be utilized more effectively by some other organization while still meeting the economic demands of the nation. If you include the governments of highly-planned economies like North Korea, the ex-Soviet Union, or China during the Mao's older years, then these could be considered examples of this.
I hope that answers your question.