It is only when you read into the article that you find Priebus isn't in favor of amnesty. See what he is quoted as believing the Republican consensus favors:
It means border security, it means enforcement, it means legal immigration, it means E-Verify, it means a lot of things. It means guest worker programs on the border. These are all things that are accepted within the platform of the Republican party.Let's suppose Republicans have majorities in both House and Senate after November, and pass something akin to the above. I'm doubtful the President will sign it.
I can tell you what it means for me is no amnesty whatsoever. And I've never been in favor of programs that are akin to amnesty. I think sanctuary cities should be cut off from federal funding, I think we ought to secure our border. I think Congress ought to follow through on its promise in 2006 on building the border fence.