It is not a crabgrass, however it is similar. It looks almost as 'malnourished' smooth crabgrass. It is very fine and it grows only about 6-7 inches tall and about 10 inches with the seed heads. It spreads with rhizomes and it doesn't seem to totally die in the winter. We had snow and freezing temperatures this winter for extreme 4 months, but when I raked off the snow from the grass to check it out, this weed was green at the very bottom. It was and is dead/yellow as an annual would, but it didn't die totally. It can be pulled out easily and it feels like a tiny crab legs. I can pull them out with my eyes closed, they are so different from any other weeds. And this weed doesn't seem to have issues in a shade either.

It is taking over our lawn and no matter what we use to kill it, it doesn't work. We are trying to rebuild an accidentally killed grass in a very large area within limited budged we have available these days.

Thank you in advance

I found out that it is called nimbleweed.
I already ordered TENACITY herbicide for it. It is a new product available since April 1, 2011.
http://www.greencastonline.com/TenacityHerbicide/Residential/faqs.aspx