Pretty simple, like the title says, what's the difference between いつだって and いつでも? I can tell there's a little difference, but it's so very difficult for me to pin down.
「いつだって」 is a more casual way of saying 「いつでも」 and it has a little emphasis on its meaning compared to 「いつでも」. You'll hardly see 「だって」 being used in newspaper articles compared to 「でも」.
だって source: デジタル大辞泉 (http://dictionary.goo.ne.jp/leaf/jn2/137401/m0u/)
Also this might be of your interest: http://dictionary.goo.ne.jp/leaf/thsrs/17174/m0u/