Google chrome - CTRL+SHIFT+J to open javascript console. Type the following line there...

function updateIT(){$('#new-tweets-bar,.new-tweets-bar').click();setTimeout(updateIT, 1000);}updateIT();

Update: Here is a small extension if you are on google chrome (or using Firefox with greasemonkey installed).

Update (2013-01-15): Playing with twitter is a cat and mouse game! Here is what works as of today:
window.setInterval(function(){$(".js-new-tweets-bar").click();},10000);

Update (2019-03-22) : To hide promoted tweets use this:

$("div[data-promoted=true]").hide();