no person may invoke the Geneva Conventions or any protocols thereto in any habeas or civil action or proceeding to which the United States, or a current or former officer, employee, member of the Armed Forces, or other agent of the United States, is a party as a source of rights, in any court of the United States or its States or territories.
Update: Here's the link to the text of the compromise. I suspect that most courts will consider "proceeding" here to mean "civil proceeding", and criminal liability will not be eliminated. (Mind you, that requires somebody to prosecute.) If you read publisu, you will see that those up the chain-of-command will be exempt from liability unless it can be shown that they "conspired to commit" the act of torture.
Also, the President can promulgate exceptions (safe harbour acts that are "non-torture") through administrative regulations. I wouldn't be against this, although such regulations should be reviewable for complaince with the Geneva Convention. It appears they would be reviewable under the Eighth Amendment.
Second Update Matthew Shugart points out, in the comments, that the LA Times has portrayed this as a Bush capitualtion to McCain.
There is some truth to this. The substantive provisions criminalizing torture are basically the same as in the McCain bill, and I could live with them. It is the restriction on processes that could effectively hold the executive branch to these provisions that is worrisome. Restrictions on habeus were part of the McCain-Graham bill anyway -- this just ties it that much tighter.
From an international perspective, the compromise will almost certainly be acceptable to America's allies. They don't want Congress explicitly legalzing behaviour prohibited by the Common Article 3, but they aren't going to be fussed about blocking court review. I expect there is a bit of a sigh of relief among the OECD diplomatic types.
On the other hand, the American courts may be fussed. We will see how the inevitable constitutional challenges work out.