Even shorter than a boosted weapon. You're talking about a polonium neutron source, and those needed to be changed about once a WEEK for reliability, and were completely useless after only two weeks.
The "gun-type" SADM still used a pretty hefty D-T neutron source, and it still had a nasty tendency to fizzle. An implosion-based weapon would be a great deal more reliable.
If he's got a tritium-boosted suitcase now, it sounds like he still has a wide time window of opportunity. Far too wide.