For 1999 the total number of operators on farms with sales of $10,000 and above is given as 949,000, but the total number for all farms is given as 1,912,000. Also, of that number 165,000 are said to be female, which suggests that family members are not counted. So even without the undocumented workers we're looking at several million workers, bringing productivity down to around 50 per worker. (OK, that's a very rough guess).
A very rough guess indeed. The not-counted family members range from the preteen who tends a few chickens or pigs and such, to the spouse who does some farm work while simultaneously managing all the myriad details of household and family affairs, to the adult offspring or in-law who's running the harvester and doing a full day's work alongside the owner-operator. Very hard to estimate. Undocumented farm workers are estimated at a quarter to a half million or so. I don't think you're going to make "several million" out of all of that.
Then you have food imports. In 2009 the US imported 17% of the food consumed, so we're down to around 40 per worker.
In 2009, food
exports accounted for about 20% of production. We export a bit more than we import.
And then there's the other half of the question, how big a part of a population would be agricultural workers, even for a world totally dedicated to food production[*]? Start with children and retired parents of the workers. Then add the people who build the machinery that enables the agricultural worker to be so productive and their families. Then add tertiary professions catering to those workers (and their families). Even if an agricultural worker could produce food for 100 people (instead of less than half that), a population of 10 million wouldn't come anywhere near producing food for a billion people.
At 1 per 100, a food worker doesn't feed 99 other workers (or 50, or somewhere between the two). He feeds 99 other
people (or 50, or somewhere between the two), including his family. Ergo, if we go by that 1 per 100 ratio, a population of 10 million food workers is feeding 1 billion people - of whom about 20 million or so are his/her spouse and children, dependent elderly family members, etc., while those 970 million other consumers consist of about 300 million or so non-food workers (including such folk as the guys who built the tractor, the guys who process the grown food into finished goodies like bread, the guys who haul the food to market, and so forth), plus THEIR spouse and children, dependent elderly family members, etc. That puts the food worker at around 3% of the labor force under that model.
In the current U.S. (a net exporter, as previously stated), the acknowledged food worker is 1% of the labor force; factoring in the undocumenteds and other unrecognized workers, it might get to 2%, maybe 3% if we're generous.
So, that 10 million feeding 1 billion is reasonable where there's abundant land, energy and technology to apply toward agriculture.
However, while only 1 to 3% of the labor force is food workers, 1/6th of the labor force is involved in getting that food from farm to your plate: processors (mill, bakery, cannery, slaughterhouse), distributors (trucks, etc.), retailers (your local supermarket), and food services (restaurants, etc.). So, getting back to that billion, there may be only 10 million producing the food, but there are about fifty million beyond that who work with them to keep everybody fed. That leaves roughly 250 million for other professions and 600 - 700 million dependents - likely less depending on the degree to which spouses and elderly are a part of the formal workforce.