If you only have 30 or 31 days, it is possible to go from SJPP to Santiago, but does not give you the chance to smell the roses. This can be stressful too, when you feel you need to make up time, (should you miss a day due to aching bones, feet or the usual Camino ailments), or want a rest day or two in Burgos or Leon but your schedule does not allow. And stress is not allowed on the Camino!
I'm heading on my 3rd Camino starting next weekend and like you only have 30 days. I'm lucky that I've experienced both the SJPP to Santiago and SJPP to Finnisterre so don't feel any guilt about cutting out a section or two this time. It allows me to do a different start (Camino Aragones), walk my favourite parts of the Camino Francais and at the end walk from Santiago to Muxia. For me that means cutting out the Meseta between Burgos to Leon (Astorga actually). From those I've met on my caminos, the Meseta is loved by some and loathed by others. I don't feel bad about missing if it would otherwise mean that I'd be missing out of the SJPP to Burgos or Leon to Santiago segments. As far as I'm concerned those can't be missed.
If you need to cut out 4-5 days, I'd recommend walking as far as Fromista (day 15 or 16 if walking from SJPP) and in the morning (or afternoon if not over nighting in Fromista) taking the local bus/shuttle to the city of Palencia which is around a 1 hour ride. Spend a couple of hours walking the markets and pedestrian friendly shopping area before hopping one of the frequent trains to Leon. By walking at least to Fromista you'll get to experience a few days of Meseta too. From Leon you can either rest another day or pick up where you left off and enjoy some of the best parts of the Camino.
My two cents worth...