To be fair, I said I would consider an ASAP start during the interview (but still told them my preference is for 2 weeks).
They offered me a position, and while discussing my start date I kind of backtracked about starting ASAP, and said I would like to give 2 weeks. The current company Im working for is pretty big, they treated me well, and I dont feel comfortable burning bridges.
Then the HR person of the new company literally threatened to rescind the offer, and offer to somebody else.
My goodness, I get that I backtracked a bit, but this feels dirty. How big of a red flag is this?
UPDATE!: Well, the HR person ended up getting back to me and allowed me to put in 2-weeks' notice. But while thinking about it throughout the day, everything didn't sit right with me, so I've decided to withdraw.
There were other red flags during the interview as well. The same HR person pushed and asked me to describe my past health issues (I had a huge gap in my resume due to health issues, but I showed consistent work during the past four), and during our phone call yesterday, he asked for clarification again that my health wouldn't be an issue before making the offer.
All of this just reeked of desperation and unprofessionalism, so I've decided to let it go. And yes, I completely agree I could have been better with communication on my end, but the red flags on their end were too hard to ignore.
Thank you everyone for your input!