I'd give it at least another week and again two weeks after that. Not sure if the floating row cover is sufficient to protect from our sleet and ice storms without collapsing. It may work initially but once your seeds are sprouted they'll want something to climb on and full sun/bright light. Your supports you'll want to push into the soil deeper than usual to keep them erect under the weight of the pea plants plus any ice/snow/sleet on the row cover.

I've used cuts from brushy deciduous shrubs and had them topple over if the main branch isn't long enough or thick enough, especially in mounded rows of loosened soil.

We could still have this weird mix of ice/sleet/torrential rains mixed with periods of oddly warm weather so whatever you attempt for early crops is going to be an experiment. That's why I say plant a second row a couple weeks after the first.

One year I made an effort and got peas in early enough although I usually don't think about gardening this early; just lazy. They grew well. I didn't use row cover. Of course, another year, the seeds didn't even come up.

I keep mentioning the Watt Quarales planting guide here. They are a local seed company. In the piedmont, they suggest that peas be planted from the beginning to the end of Feb.

They don't seem to mind cold soil but I have had them rot when things get wet and slushy. The non-edible sweet peas are incredibly hardy, I plant them around Thanksgiving. They come up and get frozen back over and over and then they just jump out of the ground when things warm up for good. Its like they grow a ton of roots all winter long. I usually soak my edible peas until they plump and I have been known to start them indoors in pots and then transplant them after the ice storm left - they hate being transplanted though so you have to be careful.

I bought my peas a week ago and just waiting for the soil to dry out a bit. As John said they will rot when too wet. I've had success in Raleigh planting as early as late January before, but this year looks like they will not get in until mid to late February.