The race was between Romney and Obama. Romney called the President and then gave his concession speech.
I really don't see why Obama thought he needed to call these two men in the middle of the night.
It would have been perfectly logical to wait until Wednesday morning to call them. But, as others have pointed out, they should have been calling him to congratulate him on his re-election but they are too classless to do this. This would be especially difficult for McConnell since he failed at his job #1 for the past 4 years which was to deny Obama a 2nd term.
I seriously doubt the republics are going to compromise. They still think they have political clout and that the people are behind them. This despite Obama's re-election, Democratic pick-ups in the House and an increased Senate majority.
I really wonder if at some deeper level they know the demographics are against them and that their hate-driven policies of protecting the wealthy and wanting to deny minorities the same opportunities and rights as others will never prevail in the future. So this is kind of a scorched earth mentality. If you can't win then burn down the house. It is very childish but I really wonder if this isn't the mentality of today's republics.