The answer is yes. You will face some variation on the problems that OP described in his post.

The level of paperwork and pain you will face depends on (1) where you are "doing business" (and that is a nuanced phrase); (2) what type of business you are doing; and (3) the humans who are doing the work -- U.S. residents or nonresidents.

The problems arise from the multiple government entities that have the ability to impose tax on a business. From the top:

- income tax from the Federal government, (most) State governments, and (a few) cities.

- various employment taxes to fund government retirement benefits, unemployment relief, medical care for the elderly, etc. etc. This is Federal and State. Solve that problem by handing the whole f-ing problem off to a company that specifies in payroll services. Hint: despite marketing promises to the contrary, all payroll services are alike, except for the ones that steal your money. Buy services from an established, reputable payroll services company.

- sales tax. There are a maddening number of jurisdictions nationwide that impose sales tax at a maddeningly different set of rates. Some things are taxed in one place and not in another. My experience with the California bureaucracy that administers this tax is that they are the second-lowest level of Dante's hell. (The lowest level of hell is reserved for the employment tax bureaucracy).

- City business licenses. It never ceases to astonish me how stupid local governments can be. The City of Los Angeles imposes a tax on the privilege of running a business within the City limits. It is a percentage of gross revenue, FFS. Yet adjacent cities (I'm in one--Pasadena) charges a vastly smaller tax, based on number of employees. A business can save tens of thousands of dollars simply by putting its offices in the correct place. Then the City of Los Angeles has budget woes and wonders why. Oh, well. The immediately former Mayor has his name in big-ass letters in the international terminal at LAX. C-o-r-r-u-p-t-i-o-n. But I do not judge. And I am not bitter. :-)

Having said all of that, it IS possible to create an outpost in the United States and keep the paperwork and tax burden semi-sane. Assuming your business generates some kind of software, I would do the following:

1. Choose your base of operations in the USA on purely business grounds. Where are your potential employees? Where are your potential customers. Let's say it's California.

2. Next, examine carefully the different municipal governments in your target area to see which cities have the best city business license set-ups. You might find that these places are popular and rent is expensive. Go figure.

3. Next set up the business entity you need. If your company in Canada is a corporation, you almost certainly will use a corporation in the USA. (Hint: ignore everyone who tells you about LLCs. CRA treats U.S. LLCs as corporations for tax purposes. Just set up a corporation). First preference is to set up the corporation in the State where you are actually doing business. It saves you money and paperwork. Success in business is all about avoiding paperwork.

4. The U.S. corporation should probably be owned by your Canadian corporation.

5. Staffing the U.S. corporation with employees. If you are coming across the border you will need a visa. Look at the TN visa or the L-1A visa categories as the easiest way to be here, work, and live. If you are hiring locals, you don't need a visa for them, obviously.

6. F-ing payroll taxes. Hire a giant-ass payroll services company. I have used one after another and they have all f'd up my payroll at one point or another. F-ing Intuit's f-ing QuickBooks Payroll is the worst. "Oh, we really can't track that $120,000 and can't really tell you where it went." But I am not bitter. Really. Not much, anyway. :-)

7. Hyper hyper critical for you coming across the border and working here: payroll taxes. You have to contribute to the U.S. Social Security system with your taxes even though you will never get a penny of benefits here. There is a treaty with Canada. Look for "totalization agreement" in your favorite search engine. You can eliminate U.S. Social Security taxes for 5 years using that method.

8. Your business SHOULD -- for certain definitions of "should" -- pay income tax to the Federal government and the State of California. If you have a sufficiently high level of business activities in other states, they will want to impose income tax on your profits, too. Strive to avoid those activities in the other states. That's where you need guidance.

I hope that helps. My email is in my profile.