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Whilst objectionable, I don't think Giuliani is stupid - it won't have been an accidental reveal, and I'm sure he appreciates exactly the likely consequences of the admission.
Presumably there's been some calculation that admitting to it now is less painful (or stops off an avenue of attack for Mueller) than allowing it to carry on or being forced to open up about it later.
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I imagine someone within the Republican hierarchy has a large wall calendar with the Mid-Term elections multiply highlighted. Previous TeamTrump actions/lies/mis-leading statements are being measured on a damage now versus damage in the run up to the elections.
Maybe 6 months is thought to be long enough for fundamental Christian Trump voters to forget their guy paid for sex with an adult entertainment star.
Giuliani appears to be doing his best to match Trump for putting his foot in it.
The suggestion is that Trump repaid Coehn the $130,000 cover up money, but of tranches of less than $10,000 in order to avoid reporting requirements. A crime in itself, reportedly.