I think its fungus. In the first close up photo you can see how it is forming threads, eggs don't do that. The mass coming from the plant stem is definitely not an egg sac.
I'd clean up as much of it as you can. A simple jet of water from the hose will clean up a lot of the mess.
And then I'd wonder where the mass coming from the stem originated. Is the stem cracked? Have you had a really wet couple of weeks?
