Members of the public are being urged to help save lives by facing their fears and following instructions on the park's website to safely capture the spiders.
"Twenty-sixteen saw the least amount of hand-ins in the park's history, despite good exposure and community awareness," park ranger Mick Tate said. "Should supplies continue to diminish the lifesaving antivenom programme will be in jeopardy."
A woman asleep in her bed in the Southern Highlands and a Taree resident were bitten in recent weeks, compared with no reported bites in the same period last year.
Funnel-web spiders are known for their highly toxic and fast-acting venom but no deaths have been recorded since the antivenom programme was introduced more than 35 years ago.
Meanwhile, Sydney is on track for its hottest summer since before federation.
If Sydneysiders are subjected to one more day above 35C, the ninth this summer, it will equal the record set in 1896.
The city has already set a new record for hot nights, with the mercury staying above 24C four times, two more than the summer of 2010.
Sydney is forecast to reach 38C today, and the city's west is expected to hit 40C in the afternoon.
"We'll most likely be standing at eight days [above 35C] by the end of today with a fair bit of the summer to go to try and at least equal that long-standing record," Bureau of Meteorology forecaster Rob Taggart said.
A cool front from the Southern Ocean will offer Sydney short-term relief later today, with the temperature dropping to the mid 20s.
- AAP
