Thank you for your post.
What version of FileMaker Pro are you using? What operating system? What version of the operating system? What browser is being used?
With FileMaker Pro 10 on Mac OS X 10.5.8, I created a Test.fp7 database file that includes a few fields. On the layout, I entered 300+ characters and sized the text to fit within six inches. The contents now shows on four lines. I turn on Instant Web Publishing.
On a Windows XP SP3 machine, I launch Firefox and access the hosted file, and I'm able to see all four lines of the text box.
Please let me know what I'm doing differently than you, and I will try to replicate the problem here.