Yeah, in order to be that small they depend on tritium (hydrogen isotope) which has an eight year half life. Anything from the Soviet era would have to be refurbished to be useful.
With the porous Mexican and Canadian borders and shipping, a normal size nuke might not be that difficult to bring in or even make domestically.
The first time we hear of a “foreign national” brought in to a US hospital suffering from radiation sickness, then we will know the time is short. Hopefully we will still be able to interrogate that guy.