Are you talking about the default Search bar, or the one on the Google Toolbar (extension)?

Did you move either the Search bar or the Location bar?

You only get that resizer if the search bar is directly to the right of the location bar. That places both bars in one container and allows to change the relative width of both.

Thanks. Somehow another bar was inserted (coriolis) in front of the search bar. When I removed it I was able to get the double headed arrow.

Make sure that you don't have a add-on called "Searchbar Autosizer" installed. You won't get the double arrow cursor to resize the address and search bars. Took me a long time searching to find the problem.