The Soviets were totally broke which is one of the reasons Gorbachev folded in 1989. They were literally bleeding blood and cash in Afghanistan, they were no closer to achieving any of their goals in that benighted country. They were already spending pretty much all of their actual capital and income just building and maintaining their conventional forces plus all that money on Strategic nuclear weapons which would suddenly become obsolete and useless if they could not get through to attack their targets in the West. The Soviets might decide to look at ways to counter SDI rather than build their own, they might go all in on ways to blind the early warning satellites and jam the BMEWS systems and ways to spoof the various techniques SDI was coming up with to differentiate between real and fake RV's. If their SSBN's had been MUCH quieter, were actually able to evade NATO subs and they could overcome the accuracy issues they had so they could be effective counterforce weapons then they could have launched missiles from unexpected areas like the Southern Pacific areas or the equatorial Atlantic regions, unfortunately their subs continued to be readily tracked in open waters which is why russian doctrine called for the establishment of sanctuary area where their SSBN's could lurk under cover of surface, air and friendly subs . The other option would be to build a large force of Blackjack bombers capable of carrying and launching long range nuclear armed cruise missiles, SDI would have been almost incapable of doing anything to a air launched non-ballistic weapon. The US would have needed to build a much larger ADF force (possibly much bigger than the one they had in the early 1960's) and build a lot of Patriot or some other follow on strategic SAM system.
To ensure MAD continued the Soviets only had to be able to cast enough doubt in the US's mind that the Soviet strategic missile and bomber forces would get through and cause unacceptable damage if the US attacked or if they provoked an attack from the Soviets regardless of SDI's ability. Of course the other possibility would be that there was a real risk that, fearing the loss of their ability to ensure MAD the Soviets might decide to preemptively attack the US before SDI was fully operational.