So what you're saying is that, the actual dropdown box should maintain it's 60px width, but it's ok if the dropdown list it displays expands to display the content correctly.
Well I've come across this issue many times during the production of corporate sites, and I can tell you straight off the bat there's no easy answer. IE does what it does because that's how it was made, the same with Firefox.
One client in particular, a law firm, who were very intent on having their site accessible even went so far as to use DHTML to create a label which displayed the full name of the option chosen, similar to what you mentioned beforehand. It turned out that even this wasn't good enough as it proved to be problematic, with regards positioning and useability, not to mention they didn't like the fact that it ran with javascript. In the end they removed it and realised that the use will probably be able to work out what the option was tehy were selecting because they could read enough of it.
In your case however you've only got 60px to play with, I couldn't find an example in the link you said of a description so I can't really visualise the problem you're having but I would say that you shouldn't try and reinvent the wheel, and try and use the right tool for teh right job, the way it was intended to be used.
Hope this helps.
Cheers,