How bad it is using the same IV twice with AES/GCM?
Even a single AES-GCM nonce reuse can be catastrophic.


A single nonce reuse leaks the xor of plaintexts, so if one plaintext is known the adversary can completely decrypt the other.  This is the same as for a two-time pad.
In messages up to $\ell$ blocks long, after a single nonce reuse the adversary can narrow the authentication key down to $\ell$ possibilities with polynomial root-finding and thereby forge messages with high success probability $1/\ell$.


How?  An $\ell$-block message is a polynomial of degree $\ell$ with zero constant term; the authenticator under secret key $r, s$ is $m \mapsto m(r) + s$, where $r$ is reused between messages and $s$ is derived as a secret function of the nonce.  Find authenticators $a = m(r) + s$ and $a' = m'(r) + s$ for distinct messages under the same nonce, and only the ${\leq}\ell$ possible roots of the degree-$\ell$ polynomial $m(r) - m'(r) + a' - a$ in $r$ are possible values of the authentication key.



Use 96-bit nonces; if you don't—if, instead, you use smaller or larger nonces—it will be as if you chose nonces randomly, and the number of messages you can safely handle drops dramatically.  But you can, of course, pad, say, a 64-bit nonce into 96 bits: what matters is only that the nonces be unique.

If the cost of a >32-bit nonce is prohibitive, you could periodically rekey.  For example, if you first establish a long-term key $k$, you can use $\operatorname{HMAC-SHA256}_k(i)$ as the key during the $i^{\mathit{th}}$ epoch, where each epoch covers four billion messages, and $i$ is encoded into a bit string in some canonical way.