i dont think it is possible, you will need to choise a string quote.. you cant use both.
if you really really really needs to use both of them, try to add text with java script..
something like
body ... onLoad='document.formname.textfield.value = (itself) + 'double quotes' + "singlequotes";
i have no problem adding //// or \\
and i dont tested it, i cant imagine the sort of problems you can get when trying to retrive this field value.
good luck