Obama can sign it, but the Senate has to ratify it with a two-thirds vote, IIRC. When the costs and limitations on our freedoms are presented during debate, I don’t see that happening. Obama will no doubt try to implement it in the meantime with executive orders that can be rescinded when a non-Marxist president takes the helm.
All Obama has to do is to accuse the Republican senators as being racist for rejecting him and they will acquiesce and sign it. White guilt has its privileges.