D&D 5E (2014) Your CR limit for an average 1st level party?

[Li Shenron]

Party size matters too. I would not put a party of four against a CR 3 monster. I would put a party of five against some CR 3 monsters, like some Hatchling Dragons, but ONLY as the last fight in the adventure, since they will need a long rest to recover from it. I would be more willing to put a party of six against most CR 3 monsters. I would be willing to put a party of seven against two CR 3 monsters, but not at the same time. "An hour after you have defeated the evil Dragon [apply the benefits of a Short Rest] her twin sister flies into the room. Roll for Initiative!"

Yeah I see that, but still I think the original idea of CR is to indicate the risk of sudden death (which is an individual matter, not a group matter) plus the possibility of blockers such as immunities that can make a PC ineffective to fight the monster.

Party size is taken into account by the XP budget, which indicates the difficulty category of an encounter and the total XP very much depends on how many PCs are in the group. Higher CR creatures of course add more XP against the budget, but the same CR creature is still as deadly with a single turn of actions against a single target whether the target is alone or with 10 allies.