Any glysophate product will almost kill any plant it contacts, that is supposedly what is is for. However, many plants have been developing resistance to these products and some have even gotten the gene that made some plants resistant to these. There is never any really good reason to use this stuff since there are other ways, less environmentally harmful, to get rid of unwanted plants.
One of the better ways to eliminate crab grass is to grow a good, healthy stand of a more desireable grass, but you also need to know if you have just the annual crab grass or the perennial crab grass or both.
To start growing a good, healthy lawn that will crowd out this crab grass get a good, reliable soil test so you know what soil nutrients are there and what the soils pH is. Correct any problems found and determine also how much organic matter is in your soil and increase that too. Then seed in, or sod, a turf grass that is a good match for your climate, and feed, water, and mow that grass properly so it grows in thick and lush and crowds out the crab grass. The annual crab grass needs a fairly warm soil temperature for the seed to germinate so a thick stand of grass, cut long wil lshade the soil and prevent that.

Thanks for the advice, but the problem is that the "lawn" is covered with crabgrass, as is the garden. I have a 15' x 15' spot that I'd planned to plant vegetables in, but it is completely covered in crabgrass. I appreciate that it would be ideal to garden in a less environmentally harmful way, but that's really not an option at this point.
I don't know for sure if the crabgrass is annual or perennial, but I don't think it died this winter. It seems to have multiplied since last year. The yard has been neglected for well over a decade, as the previous homeowners were quite elderly. It's obvious they took great pride in this yard at one point (they lived here for 50+ years), but I think the care just got to be too much as they grew older. :-(
I would like to give the yard as much love as they did, but it's difficult when you're starting from scratch. Worse than scratch! The idea of nursing a small patch of grass to maturity and then waiting a few years for it to take over the crabgrass is not appealing.

In the 15' x 15' spot you can repeatedly pull up the crab grass over the summer and then mulch in the fall. For the lawn you either go Kimmsr's route or start over or go chemical and over-seed. There is no perfect solution. If you have money to burn, pay the pros (real pros and not the usual gang of idiots that most people hire) to strip the existing sod and re-sod with an appropriate turf for your area. In early spring you can put down a pre-emergent to to minimize the next generation of crabgrass. Corn gluten meal is supposed to be the enviro-friendly way to do that.