As someone who uses both the late morning train on the chopping block and weekend service, I guess I'm OK with this. I have enjoyed the "W@H, show up when you want to" dot-com lifestyle from time-to-time, but I can let that go to keep my weekend jaunts with Nathan!
As to Gilroy service: it's a long way to Gilroy and ridership has been low ever since the 101 was widened. This is not to say that it should be abandoned, but it's really a separate undertaking from CalTrain's core SF<->SJ service. CalTrain should ask Santa Clara county to kick down a little extra to keep it going.
(But it does seem like the part of CalTrain between Tamien and Blossom Hill, at the south edge of SJ, could be considered part of the core system, and should be kept, even though it currently only gets served by trains going to/from Gilroy, and gets no weekend/off-hours/countercommute service at all).
Dropping Gilroy would put a kibosh on Monterey Count's plans to extend CalTrain to Salinas, although I haven't heard anything about this for quite some time anyway. During the housing bubble, there were no doubt people leapfrogging past Gilroy to cheaper digs in Salinas, but these days probably not so much. From the perspective of Bay Area residents, it would be nice to see this come to fruition in conjunction with Monterey county's proposed coastal (diesel) light rail, since together they'd make it possible to get to Monterey by train.
Anyhoo--the other part of CalTrain's proposed budget solution is another increase in fares. Regular riders don't complain to much about fares; overall, it's still a pretty good deal for commuting. Casual ridership might dip a bit. At $5+ a pop buying tickets for a whole family starts to get pretty pricey, and I'm sure that's cutting into ridership of the weekend trains that CalTrain is fighting to keep running.