My colorspace is synced through Bridge, in sRGB mode in both InDesign and Photoshop.

Syncing matches up the Color Setting's Working Spaces, but not necessarily the document assignments. Did you make sure both the ID and PS documents have the same RGB assignments (Edit>Assign Profiles...)?

As long as the doc assignments match I'm not seeing a problem in CS6—both the numbers and previews are correct.

That’s because exporting as print PDF converts RGB to CMYK

The PDF/X-4 preset would work because it doesn't allow color conversions.

I don't see any problem cutting and pasting from ID. The ID objects come into Photoshop as Vector Smart Objects, and as long as the Photoshop destination color space and assignment matches the copied object, it pastes unchanged

So, here I Sync to North American Web in Bridge, which Syncs the CS applications not individual documents:

And that updates my ID Color Settings:

But not an existing document. If I check the assigned profile of a document created with the North American Prepress preset, the RGB  profile is AdobeRGB not the  sRGB EC61966-2.1 Working Space.

It's the assigned profile that's used when you cut the object, not the Working Space. If I cut the green square and paste it into an sRGB PS document it will change even though my apps are sync'd:

I did just notice in your Color Settings for RGB that Convert to Working Space is chosen and Preserve Numbers is on for CMYK. I know my settings are both set to Preserve. Do you think this could be the reason?

You're showing the wrong dialog. You have to check Edit>Assign Profiles... in both apps (Syncing via Bridge won't change these settings).

In ID:

In PS:

It may be that your existing assignments match, but they are not set in Color Settings.

Hello Scott,

I saw your post showing a page with two columns and a table in the middle of the page that spanned both columns.  How did you do that?  I am quite new to Adobe Indesign, it would be of great help if you provided me with the details. 

Thank you,

Bill

Try the following: Export your graphics in EPS format from InDesign, then open the EPS file in Illustrator. After selecting your graphics in Illustrator choose rasterize from object menu. Then copy and select paste as pixels when you paste in Photoshop.