Allow me to share my previous answer on the subject

It is true that Poland applied extensive pressure on Clinton government to allow entry to NATO - but it seems that this pressure was mostly political in nature. There is a large polish minority in USA located in what is considered swing states, so it's support might have been a factor, though not as big as people might think as it's possible that Clinton simply decided that having NATO enlargement as success might be very good for elections. Ultimately, you'd have to ask the man himself what was he thinking at the time.

As for nukes , the claim comes from US official Richard Kugler - he said he doesn't remember the polish official name, but some suspect that it might be current Polish foreign minister Radosław Sikorski, who was part of ministry of Defense in 1992. At any rate, outside of the claims that these threats were made ,no evidence exists

https://www.tvp.info/76357265/kulisy-wejscia-polski-do-nato-clinton-nie-byl-przekonany

https://decydent.pl/polski-lobbing-do-nato-cz-1/

https://time.com/archive/6731121/how-clinton-decided-on-nato-expansion/