If your products were completely without commentary and simply trading on the celebrities' name and words for your own profit, I think you'd run into problems if you did this without permission. Generally, in California and other states (North Carolina recognizes a claim for misappropriation) celebrities have the right it control their own names and likenesses for profit, and since celebrities are better positioned to fight this fight, this shouldn't be a fight you want to pick.
Even though a person consented to having his photograph and name used in an advertisement, when a photograph of someone else appeared in the advertisement with his name attached, he had grounds for a misappropriation claim. Barr v. Southern Bell Tel. & Tel. Co., 185 S.E.2d 714 (N.C. Ct. App. 1972
I think your case is weakest when it comes to celebrities who sell their words, such as author's published quotes and musicians' published song lyrics, which belong to their respective publishers, so you'd need their consent to reprint them. Same with comedians, whose jokes are their livelihood. As for politicians, who aren't supposed to sell anything, I think as a matter of fair use commentary and 1st amendment rights, you'd have the strongest case for using their names and quotes without needing permission.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
The below does not constitute legal advice, does not form an attorney-client relationship, and should not be relied upon to take or refrain from taking any action.
Copyright does not attach to short phrases such as quotes. My short answer is that there's nothing unlawful about publishing short quotes on t-shirts (with attribution to the author) and then selling the shirts.
Copyright law is federal law and, I'm quite sure, preempts all state laws that purportedly make unlawful what copyright law permits. In my view, state law "right of publicity" and misappropriation causes of action are not applicable if the only conduct alleged to be wrongful falls within the realm of copyright law (such as the alleged wrong of reproducing and distributing a properly attributed quote on a t-shirt).
In short, so long as you heed Ms. Kosyln's warning about not using celebrity photographs (which adds a layer of complexity to the analysis) I think copyright law shields you from any claims that could be made against you by the authors of the quotes.
Longer answers to very similar questions are here: http://tr.im/qDr2 http://tr.im/qDpb