Looks like Republicans are against giving President Obama more power ..................... except when it will benefit Big Business of course.

Why should the House cede in advance of even seeing an agreement its own authority to offer amendments to such trade deals? That this has been done in the past is an insufficient answer IMO. The House always has the authority to limit amendments on a final agreement when that agreement is put before them but it is absurd to agree to do so before an agreement is even made.

Anyone want to explain why the legislative branch should hamstring themselves in this manner?

One branch of government might give another some of its powers if it wants a certain policy to be implemented, but does not want to go on record as being for that policy. Not saying that's happening here, but as a general rule anyone organization (including government) should not attempt to punt responsibility in that manner.