Are your segments on the same ticket, or separate? If the latter, I would not risk it. You would have no protections if you miss the connection; all other flights may be sold out or you might need to purchase a new ticket at full price. I do not know how Delta is about LGA these days since the slot swap with US Airways, but in the past they rather discouraged connecting there.
The biggest concern I would have is that Delta uses three different terminals at LGA. Delta Shuttle flies out of the Marine Air Terminal (terminal A), Delta Connection/Comair flies out of terminal D, and Delta mainline uses both terminals C and D. There are airside buses (exiting security, walking/airport shuttle, and re-clearing is not practical here), but these run only every 10-15 minutes at peak times, and the ride from A to D is a good 15 minutes itself. That makes a 35-minute connection stressful to say the least.
I would look over several days' worth of flights to see where your typical arriving and departing gates would be. The concourses in terminals A, C, and D are relatively short, so if both of your segments are in the same terminal, 35 minutes at 8am on a Thursday is not unreasonable— though I would have a plan if things don't work out.
On the bright side, airlines do build in standard minimum connection times into their booking engines; they have no incentive to strand passengers at hubs. You have a better chance of good weather in October than in January or July. Also, congestion-related delays (most delays at LGA are related to congestion) tend to stack up over the course of the day. An 8am flight is relatively early, so not much congestion should have built up.
On the other hand, as the saying goes, your mileage may vary. Gate changes happen all the time. The connection timetables are ambitious for people with lots of luggage or who walk very slowly. And LGA is a highly congested airport; even after landing, it often takes a few minutes for a gate to open up. So research when the next connection to your destination would be, keep your cell phone charged, and if there are any problems with your flight to LGA, be proactive in talking to an agent (phone, gate, club) about the potential misconnect.
