Possible? Yeah. A good idea? No. It's not like getting back together will fix or get rid of whatever issue it was that lead to the breakup. It won't change the fact that he obviously takes the relationship not as seriously as you, seeing as how he not only ended things under a week ago, but chose to do so via text.
It sounds with you Simply Stating 'We had an argument,' that is Will... Blow over here, dear. Give her some time to Cool down, and then, ask her if she is Into getting Together this weekend to Talk things over. Good luck. xx
Give her her own space. Then she can think about this, and what she wants. If she wants you, she'll contact you, otherwise, just leave her be. If you'd contact her, you sound to desperate and that doesn't make things easier - not for you, and not for her. You might push her back if you'd try to talk to her.