Hi Jignasha -
Sorry, in the new Google Sites it's not possible to actually embed a public queue directly, since the new Google Sites does not support custom HTML.
If you want to use the "Embed URL" button in the new Google Sites, you should paste in the link from the "Share this link via email or IM" field in the GQueues Publish window.
After pasting in this link you can click the "Add" button. However, it will just show a clickable link on your page.
If you are on the old Google Sites, then you should be able to use the code from the "Paste HTML to embed in website" field and put this as custom HTML on your Google Sites page.
I hope this helps,
Cameron