I'm not an accountant, but in the most general terms, If you are incorporated as a C-Corp, then your earnings are subject to the corporate tax rate in which case a decrease in the corporate tax rate would definitely affect you. Doesn't matter if you are a 3 person C-Corp or a 70,000 employee C-Corp.
If you're incorporated as an S-Corp or LLC -- which uses a pass-through tax structure -- a decrease in the corporate tax rate would not affect you; only a decrease in individual earned income tax rate would affect you.
(There are some edge cases as you can be set up as one type of corporation and elect to be taxed as another type).
I'd like to clarify what you say here: there are two levels of law involved in the federal taxation of business entities. First, there is the state law under which the entity is formed: a business's typical choices for state-law entities are the corporation, the partnership, and the limited liability company. Second, there is the Internal Revenue Code, which provides three basic forms of taxation: "C corporations" (taxed under subchapter C) pay their own taxes, separate and apart from the shareholders; when dividends are distributed to the shareholders, the shareholders then pay tax on those. "S corporations" (taxed under subchapter S) do not pay their own taxes. Instead, each shareholder pays taxes (at the individual rate) on his or her share of the net income. Distributions to the shareholders are not taxed, since the shareholders already paid tax on the income as it was earned. Finally, partnerships (taxed under subchapter K) likewise do not pay their own taxes, but the shareholders pay taxes (at the individual rate) on the partnership's net income. There are important distinctions between S corporations and partnerships, but they aren't relevant to this brief overview.
The Internal Revenue Code provides each type of state entity with choices as to how it will be taxed for federal income tax purposes:
A corporation will be taxed for federal purposes as a C corporation by default. If it meets certain requirements, the shareholders can elect for the corporation to be taxed as an S corporation.
A partnership formed under state law will be taxed as a partnership by default, but can elect to be taxed as a C corporation or (if it meets certain requirements) as an S corporation.
An LLC with only one member is disregarded by default (meaning that the income and deductions are all reported on a Schedule C to Form 1040, as though the business were operated as a sole proprietorship), and an LLC with more than one member is taxed as a partnership by default. In either event, the member(s) may elect to have the LLC taxed as a C corporation or (if it meets certain requirements) as an S corporation.
I wanted to clarify because (1) it makes me look smart, and (2) I have this pet peeve about people referring to S corporations and LLCs as though they are alternative structures; they aren't. They come from completely different levels of law. I understood what you meant (a multi-member LLC does default to partnership tax treatment for federal purposes, which
is an alternative to S corporation treatment), but I prefer that things be stated clearly.
EDIT: A corporate tax rate cut would only affect (directly) entities taxed as C corporations, since, like I said, entities taxed as S corporations or partnerships don't have a tax rate.