I read today the opposite, apparently US Intelligence are not expecting any major successful Ukrainian offensive and instead warning about Russians preparing new major offensive at the start of next year toward Odessa.
Anyway, even if some major Ukrainian success happen, that would be perfect excuse for Putin to proclaim general mobilization, apparently political situation is such that this "war" is still not seen seriously among peoples in major Russian cities like Moscow and St.Petersburg, so its still impossible for him to start full mobilization.
According to Russian casualties list, big part of their dead and wounded actually coming from Asiatic part of Russia like Buryati ethnic group for example, so Muscovites and likes still not losing their sons and brothers. Also men from those two self proclaimed Republics are being used as cheap cannon fodder.