There's a few things that can cause that particular error. When you've got a chance check to make sure that Windows and your graphics drivers are all up to date. Sometimes having out of date drivers or software can cause this error.
If you're still getting it after that try setting up a Clean Boot on your PC to see if that helps. If there's another program running on your PC that could be blocking Origin that might help get around this. You can find more info on how to set up a Clean Boot over at the EA Help website.
Let me know if you're still getting the same error message after that. Thanks!
I'm wondering if this is actually a connection issue in that case. It may not be something within the Origin client itself.
When you have a chance can you try running through the connection troubleshooting steps over at the EA Help website? If you're still having any trouble after that check out the PC-specific steps as well.
Let me know how that goes when you have a chance.