i think it could be dodder. my grandfather used to call it "love vine" or "love-something" because it wrapped around everything and smothered tender annuals. those on his plants were more of a yellow color.
there is an image at the link below but a web search will yield even more of different species.

Here is a link that might be useful: dodder -cuscuta europaea

a better link below.
it may very well spread to other areas of your garden.
you should try to eradicate it and the host plants, if possible.

Here is a link that might be useful: dodder spp.

Yikes!! That's it exactly! I certainly appreciate your help, but now am all anxious about getting rid of it. It is particularly insidious because you cannot see the rooting really. And they call this thing "love plant"!!??. I agree w/ the other names on the site: strangleweed, devil's-guts, goldthread, pull-down, devil's-ringlet, hellbine, hairweed, and devil's-hair!! It does seem to be very localized in my garden right now & I will go out and look for the host plant--I think it is mainly in the groundcover phlox (that's also the last thing I planted there (even tho it was just a transplant rooting from across the yard).

Has anyone else tackled this fiend and can offer advice?