It was a hard fought battle, but I came up with a way to do this without any requirements for styles on the container at all (including its font, alignment, etc.).
This is not a perfect solution, but hopefully it works for your purposes.
var
    //Keeps the content (individual spans) as they are built.
    $keeper = $("<div>"),
    //Used to measure span width for comparison to container.
    $measurer = $("<div>"),
    //The container of the text content
    $p = $("p"),
    //An individual line of the content
    $line = $("<span>").appendTo($measurer),
//make this "invisible," but allow for measurement against container width
//with no restriction on measurer's own width (fixed)
$measurer.css({'position': 'fixed', 'top': '100%'}).appendTo("body");
//Iterate through each "word" derived from splitting on any space.
$p.text().split(/\s/).forEach(function (elem) {
    //Start forming line text.  Don't forget word spacing
    $line.text($line.text() + elem + ' ');
    //Enough words to make the line width longer than the p width.
    //This indicates the end of "line."
    if ($line.width() > $p.width()) {
        //Remove the last word.
        $line.text(function (_, text) {
            return text.slice(0, text.lastIndexOf(elem));
        });
        //Keep the currently formed line to add back later
        $line.appendTo($keeper);
        //Create a new line for measuring
        $line = $("<span>");
        $line.text(' ' + elem).appendTo($measurer);
    }
});
//Append any leftover words not big enough to form a whole line
$keeper.append($measurer.html());
//Add back content
$p.html($keeper.html());
//cleanup
$keeper.remove();
$measurer.remove();
http://jsfiddle.net/6Cx3h/2/
You can also do this on window resize in case the container's width is window-dependent.
(you can see my attempt using height instead of width at http://jsfiddle.net/6Cx3h)