What kind of Ivy are they smothering? That might be a good thing, LOL!

I don't think they would smother ivy. I doubt there is much that can smother ivy :-)

the marsh marigolds are somewhat of a spring ephemeral, they bloom early and then disappear... so your other ground covers should thrive while the marigold is dormant...

Probably not marsh marigolds but the extremely invasive creeping double buttercup. They will smother everything. Try roundup.
Another case when the common name is not an indication of what you have.

I believe what you have is lesser celandine, which is considered to be an invasive. Check here for a picture: http://www.nps.gov/plants/alien/fact/rafi1.htm. The good news is that it is a spring ephemeral, meaning it will soon disappear (only to reappear next spring). Because it covers the ground densely, it will crowd out any native plants that are trying to get established in the spring. I had it covering my entire back yard one year, and until it died off, I didn't have to do any mowing, so I guess it does have that as an advantage, but really no one should be planting the stuff, as it escapes into natural areas and takes over. It is quite common in SE PA.

I saw it at the Cincinati Nature Center - the woodland garden of Mr. Krippendorf. It had completely carpeted a large woodland area - nothing, but nothing could grow up through it.
When I was given a few plants by a friend who said her sister's garden was full of it, I thanked the giver and pitched the plants. This is a horrendous weed.

Please Help! These little plants are taking over my lawn. I spend an awful amount of time and money to make my grass look nice but they are really starting to spread all over. I have one huge spot and then a bunch of smaller areas all over the place. How can I kill them off for good. I have tried scotts weed plus 2 and a diluted water and weed killer solution but there still there. Please Help, Anthony

Lesser celandine actually smothered what had been a nice dense bed of japanese pachysandra on my steepest slope.

To kill lesser celandine is a job and a half. My neighbors and I are on a mission to erradicate as much of it from our yards and the part of Rock Creek Park in DC we back up to as we can.

Here's what we've found works the best.

Use double or triple strength Round up (you buy the concentrate and mix at double the recomended rate; lesser celandine laughs at the regular rate) into a sprayer (the gallon size Round up that comes in a sprayer with some of the concentrate added works well).

Then spray the crap out of the plants, soaking all of the leaves (any you miss will not die.) This is best done before about 2 pm because Roundup works on actively growing plants best. A week to two weeks later, spray again. About a week later the plants will turn yellow and die.

Repeat next year or hand remove the stragglers so they don't form new colonies.

I try to do my spraying early in the spring before anything near the lesser celandine breaks dormancy. Otherwise use a section of newspaper or cardboard to shield the other plants from the Round up spray.

This about the only thing besides poison ivy that I use weedkiller on.

I agree, you don't have marsh marigold. They don't have bulbs and they aren't small plants. Mine is two feet wide and has never seeded or spread. It is at least five years old.