Almost none.
Verizon has all but stated they're not interested in carrying another Nexus phone, since it's "incompatible with their business strategy" (ie, they can't control updates on it and install bloatware on it).
As for the Nexus 5 itself, the leaked FCC diagrams show that it doesn't even have the correct radios to work on Verizon's network.
> If it's not.... it's gonna have to be a super great phone to convince me not to get a different comparable phone on Verizon.
I haven't found any other phone on Verizon compelling enough to make me consider upgrading to a Verizon phone from my Galaxy Nexus. When the next Nexus comes out, I'm probably ditching them for T-Mobile, even though I still have unlimited 4G data on Verizon.
I'm just completely fed up with Verizon's inane moves to keep all phones on their network locked down (they even forced the HTC One bootloader to be locked). No more.