I am a little bit tired right now (out of coffee), so I am unable to figure this out.
When I set
p.style.width = auto
width:auto defaults to 100% (that is, minus borders and paddings, see here), if you are not in a floating / positioned environment. Actually, without
you're quite out of luck setting the width of an element to a minimum in CSS only. See, e.g., here for how you could achieve it in Firefox (only).
Edit: You could also use
display: table; width: auto;
but, for one, this is also not supported in all browsers and then the table design may bring you in all kinds of other trouble.
Edit 2: You might, as suggested by DisgruntledGoat, also try
display:inline-block. This page gives a cross-browser implementation targeting IE6+, FF2+, Safari 3+ and Opera.