No, it's pretty much the same for a sole proprietorship as well. The business is taxed using Schedule C on your 1040 form. You pay taxes on the net income after expenses. You don't have a payroll in that case (no employees), but any money that you pay out to sub-contractors or use to purchase expense items is tax deductible. If you buy capital equipment you can, with some limitations, choose to expense it or depreciate it over time. In either situation, the money spent on the equipment is tax deductible over one year or several.
The point of "pass through" taxation, whether for a SP, LLC, or S-Corp, is that the net income of the business is only taxed once. Every dollar that comes in either goes out as expenses (and is taxed as income for the vendor/contractor) or is paid out to the owner as profit and taxed. With a C-Corp, the company pays taxes on its profit, and then the owner/employees pay taxes on their distributions. Money paid out to employees or vendors is still only taxed once, as far as I know.
Anyway, this is all kind of beside the point. If I'm a small business owner and I rely on my company's profits to pay for my room and board, then I'm going to expect to take a certain amount of money out of the company every year so I can feed myself and my family and keep a roof over our heads. The dollar value that I need to take out of the business every year has a lower bound determined by my personal expenses. Let's say that number is $300,000, and let's also assume that I routinely meet or exceed that number most years.
Now, what happens when my taxes are increased? I still need to net at least $300,000, but now more of my top-line is going to the government in taxes. Now I need to take out at lease $325,000 to get the same after-tax take home pay as before. In order to meet my needs, I either need to increase sales or decrease expenses to make up the difference. If the business cycle is on the down swing, then I may not be able to increase sales enough to cover that additional tax burden. The only options left are to cut business expenses or to live with less take home pay. Hmmmn. Maybe I can live without a secretary, or perhaps I could eliminate a position and get more hours out of the remaining employees. I'll probably save on overhead even if I have to pay more for the hours worked.
Hey, it's easier than telling my kids they're not going to Disneyland this year, right?
By the way, I'm not arguing for or against tax cuts or increases here. It just seemed that the way people were framing the discussion wasn't helping anyone understand the issue.