Q:

Why can't I enable SSHv2 on my Cisco 3750X?

It seemed simple enough:  use ip ssh version 2.  
This was the result:
3750xCoreStack(config)#ip ssh version 2
Please create RSA keys to enable SSH (and of atleast 768 bits for SSH v2).

3750xCoreStack(config)#cry key gen rsa
% You already have RSA keys defined named 3750xCoreStack
% Do you really want to replace them? [yes/no]: yes
Choose the size of the key modulus in the range of 360 to 4096 for your
  General Purpose Keys. Choosing a key modulus greater than 512 may take
  a few minutes.

How many bits in the modulus [512]: 2048
% Generating 2048 bit RSA keys, keys will be non-exportable...
[OK] (elapsed time was 65 seconds)

3750xCoreStack(config)#ip ssh version 2
Please create RSA keys to enable SSH (and of atleast 768 bits for SSH v2). 
3750xCoreStack(config)#

So, I definitely have a 2048-bit RSA key, but it tells me that I need one in order to enable SSH.  SSHv1 is presently working.  Software is
Cisco IOS Software, C3750E Software (C3750E-IPBASEK9-M), Version 15.0(2)SE7, RELEASE SOFTWARE (fc1)

Any thoughts?

A:

Thanks to both @Michael Hampton and @Dan for important pieces of information.  The ip domain-name was already set, but when I enabled SSH by using the keypair name, that worked properly.  
So, in short:  if your router has RSA keys generated, but won't enable SSHv2, enable SSH with the name of the RSA keys, like so:
ip ssh rsa keypair-name <name>

and then
no ip ssh version 1

Thankfully, this was a lab setup so no SSHv1 traffic was publicly sent, and no actual passwords were used, so mitigation from using a bad SSH version was minimal.

