You are responsible for paying taxes in any jurisdiction in which you have sufficient nexus to justify taxation. For individuals, residence is the generally accepted means for establishing residence, but some states also use employment as a nexus (such as New Jersey). For businesses, nexus is much broader, and generally includes any state in which the business is incorporated or registered to do business, any state in which it has facilities or employees, and (for sales and GST taxes) generally any state in which a customer is located.
The Chicago tax would be most similar to a sales/GST tax. Under well-established state and local tax principles Netflix, et al, could generally be required to collect the Chicago tax on sales/services to Chicago customers.
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Yup.
> For businesses, nexus is much broader, and generally includes any state in which the business is incorporated or registered to do business,
Yup.
> any state in which it has facilities or employees,
Yup.
> and (for sales and GST taxes) generally any state in which a customer is located.
Nope. That may be a sufficient nexus to satisfy due process, but it is not a sufficient nexus for the dormant commerce clause. See Quill Corp. v. North Dakota, 504 U.S. 298 (1992).
It will become sufficient if Congress ever passes and the President signs the Marketplace Fairness Act of 2015 or something similar, but that bill is a long way from that.
Note "collect sales tax." In at least some states, e.g. Massachusetts, residents and (I assume) businesses are asked on their state tax returns to report out-of-state purchases consumed within the state on which they are then responsible for use taxes equivalent to sales taxes.
Since they've decided to pursue a business strategy that has them paying sales taxes, they're pushing for an agreement that has competitors paying taxes even without a presence in that particular state.
For example, a business with offices in California and Nevada must collect sales tax when selling mail-order stuff to California and Nevada addresses, but are not required to collect sales tax for selling mail-order stuff to the other 48 states.