Hmm, this is a good brainstorming question, so I'm going to make a bunch of assumptions, based on as much evidence as I can garner—although quite frankly this is a difficult thing to reference and perhaps can only be guess-timated in the absence of textual-historical evidence.

First off, we're dealing with not just a single viking but also with the community that supports him. At least one person will be dedicated to making textiles, or about one or two sets of clothing each year, plus bags for transporting flour to feed the viking and sails to carry him to his destination. Then you'll need blacksmiths and shipwrights, although (and these are total guesses) you'll only need about two blacksmiths for a crew of thirty vikings and maybe two boat-building specialists, and these might be lent out to other communities or augmented with shipwrights from neighboring communities, depending on whether a boat was being built or simply maintained. You'll also need at least one or two craftspersons or slaves to help out with all the other daily activities like tending the sheep that provide wool or making pottery to cook and store food in. Plus there needs to be a woman who commands the farm and its wealth, usually even when her viking spouse is at home. So that's a bare minimum of about five people supporting our viking warrior, each of whom requires food. Based on production estimates, I'd wager that these five people need about eight to ten people tilling the fields that feed them (as well as the farmers themselves), and that this community of perhaps sixteen people would depend on perhaps six children and adolescents and maybe an additional two infants just to sustain their small community.

This brings us to somewhere between twenty and thirty people to support a viking, which is roughly equivalent to one good-sized farmstead—a longhouse with perhaps a few out buildings. Of course, a wealthy viking could support a few boys from lesser families, and some hangers-on would also attach themselves to successful troops, depending solely on the generosity of their comrades and their victories in the field. It's also hard to estimate just how entangled the average farmstead would have been with the fledgling towns of the Viking Age, but it must be kept in mind that these very important centers of commerce and crafts rarely numbered more than a thousand people. Overall, however, I'd guess about twenty-five people were behind each viking raider, although some vikings would come from wealthy farms and others would have poor resources and be pirating in hopes of increasing their own worth.

How many such micro-communities could Viking Age Scandinavia produce? Enough. Especially if seasonal raiding helped take the pressure off Scandinavian producers of grain and textiles. Some older studies suggest that Scandinavia was a rough place to live, generating a rough-and-tumble people, and pressuring them to adventure their lives in search of new lands. In fact, climactic studies now show that Scandinavia was increasingly inhabitable during the Viking Age, and pollen studies suggest that farming was encroaching on old forest lands. In short, viking raids were probably a projection of Scandinavian strengths rather than Scandinavian shortages. There was a lot that went into supporting a viking, but the early war parties of three or four small boats could be easily supported from a Norwegian fjord or two, or perhaps from a small stretch of the Danish coastline; whereas the later armies of the Viking Age portrayed in Cornwell's Saxon novels would probably have marshaled the resources of a more extensive logistical infrastructure, demanding intensified agriculture and textile production, which seems to be indicated in the pollen record as well.

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There's no easy reference for such a hypothetical question as this—we simply lack definitive evidence—but such evidence as we have is most succinctly summarized in: James Barrett, “Rounding Up the Usual Suspects: Causation and the Viking Age Diaspora,” in Atholl Anderson, James H. Barrett, and Katherine V. Boyle, eds., The Global Origins and Development of Seafaring (Cambridge: McDonald Institute for Archaeological Research, 2010), 289-302.

I haven't read more than half of The Last Kingdom, so I don't know exactly how big the armies Cornwell imagined or how poor he decided the land was, but if he thought the farm land was poor or in short supply, he's dead wrong. The evidence is that farmland was increasingly available in Denmark from the Vendel Era onwards, a trend that continued right into the High Middle Ages. The population of Denmark has been estimated at 500 000, which indicates a very high degree rural development. The combination of the rapidly increasing agricultural land and the high population density means that there would easily be enough support for quite large armies for the period.

For instance, using /u/textandtrowel's suggestion of 25 people supporting each viking, 20 000 warriors could have been supported. It's unlikely that there were quite so many vikings in any one force, as this would be 4% of Denmark's total population. 5000 vikings, 1% of the population, is more likely and would amount to over a hundred ships if we assume that there were at least an equal number of small and large ships, or over eighty if we assume they were large, sixty man ships.

Now, for a final point, I want to stress that Bernard Cornwell writes historical fiction, and that while he does do more research than most, he does have a number of habits and biases that distort the history he writes. Cornwell is very much a believer in writing about the "Dung Ages". That is, making everything as bleak and awful as possible. To this end, he's grossly distorted Keegan's opinion on the role of alcohol in warfare, greatly reduced the average lifespan of people (half those who lived to 20 could expect to live to 40, so it wasn't exactly rare), lowered the average age of marriage (20 wasn't exactly rare, and 14 was quite young, while the average age of marriage would probably have been 18-20), and dental health wasn't anywhere near as bad as Cornwell suggests. In this case, Cornwell was almost certainly aware that there were other possible explanations for viking raids and emigration, but chose the "poor and limited farmland" option because it fit best with the history he wants to write.