The 12th and 22nd seem to make this a non starter. But the Democrats would argue that Obama could be elected vice president, since the laws and constitution are silent on the specific issue of a twice elected president running for VP.
The laws and constitution are quite explicit on the issue of VP and President
If you are barred from serving more than two terms , you are constitutionally barred to be VP
“...since the laws and constitution are silent on the specific issue of a twice elected president running for VP...”
No, it is not silent when it specifies two terms or no more than ten years. Being a vice-president can not shoe horn more than the ten years into the intrepretation of the law.