Need help. Getting anxious.

Hello, I told this org my notice period is 30 days as I had an official buyout clause. Now my manager is not releasing me early and I got the offer from the org. I talked to them and even though HR's tone felt like they'll be okay with 60 days as well but she keeps saying try to reduce it again and again. I put my papers down as well. Getting anxious, will they revoke offer letter really? Lwd is 5 september. She's saying to atleast join in August. I talked to HR and she said "what if someone else joined earlier, we might have to drop the offer. I'm not saying we do that but just try to reduce it" I feel like she's bluffing by her tone. Don't know what to do please help.