Such global sympathy is always short-lived. Give it a few days and the trend would shift, public attention would go to another crisis. That's the nature of things. So inasmuch as global opinion is concerned, I should think delaying is counterproductive. Use the goodwill while it's there, deal with the unavoidable criticism later.
Hamas and Hamas leadership has been 'boxed in' for years. If it was that easy to simply pick them out without civilians being hurt, it would probably have been done by now.
As for political expediency, there's that, especially on the domestic front. But there's also a regional element - in the ME inaction is often interpreted as weakness. Perceived weakness leads to adversaries being motivated and more confident to attack. Some of what's going on is a message sent.