"People won't be able to access our site" sure helps but being unable to put a date on it still reduces incentive (especially when Management get involved, and especially if there is a financial outlay involving firewalls etc.).
Geoff generously provided a probabilistic sense for RIR runout: http://www.potaroo.net/tools/ipv4/rir.jpg Pick your RIR and plot its runout date. If it's ARIN, then the first ISP is out of IPv4 addresses at most three months later (since ARIN now allocates for three months' need). Of course, if demand increases, these dates might change. Will users be unable to reach your content on $RIR_runout_date + 3? They might have to get there through large-scale NAT. That might bother management if you rely on IP geo-location, or need to initiate connections downstream, or rate limit per IP address, or have anti-DOS techniques measuring hits per source IP address, or have employees VPN in, or need to report intrusions, or any of the many problems widely documented. Oh, and when I said to pick your RIR, I meant the RIR of users who access your content. Lee