And obscure the content when the text wraps
You can say left:0 right:0 but you would need to ensure that overflow:auto is also set for the fixed element but then starts to look a little messy. You can also top:xxpx and bottom xxpx but once again overflow would need to be set to auto.
Fixed elements are best at fixed widths and in small doses. I've been working with a fixed header for the last few months and its a real pain as its in a fluid site and when the text wraps it obscures the content so I've had to set a number of media queries to move the content away from the header at widths that its likely to wrap which of course doesn't help with text re-size. I've had to use a script to monitor the headers height and when it increases or decreases then I change the padding on the content underneath. Lastly when the header is too narrow for its content another media query switches it back to non fixed. All in all its a real pain although it looks nice.:)