Is tithing or almsgiving obligatory in the new covenant?

No, tithing is not required of you. I would not tithe in the new covenant, precisely to show that it is not required. Tithing was an Old Testament requirement of the Jews, whose whole government, politics, and employment were wrapped up in a theocratic society. In order to keep a theocracy going, everything had to be done legally, and just as we pay our taxes now, they paid their tax by tithing: ten percent, and it never went up. That was the taxing system of a theocracy, and it has nothing to do with us. The only thing we are to do is model our behavior on the giving of the people of the Old Testament to their established religion. How much you give depends on the person. In their agrarian, tribal society there were few truly rich people, so giving was modest; later, under Solomon, who was receiving 666 talents of gold a year, they became rich, and you saw what it did to him. So the bottom line is that tithing is not required of you.