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The thing is, they got all that "uninterrupted access" without tinkering with Miranda, because the guy was cooperating, and he waived his rights. If they're not talking, that access doesn't matter anyway, because they're not talking. So what's the issue?
The government released a slightly redacted letter yesterday, dated May 12, from U.S. District Attorney Preet Bharara to Judges Loretta Preska and George Yanthis explaining why Times Square bombing suspect Faisal Shahzad was kept in custody so long without seeing a judge or a lawyer:

Bharara also mentioned that the interrogation appears to be going well:

But here's perhaps the key point for the administration, in terms of the argument for easing Miranda requirements:

-- A. Serwer