Actually you may be surprised that you're incorrect. This is from Wikipedia. From the 380 plus KNOWN descendants who immigrated to America, it is estimated that 150 million of us are descended from one of them. So theroretically, half of the US is descended from royalty. Now, I'm not saying that this really means anything special - we are not going to be called on like John Goodman (King Ralph) to fill in if the Royal families of Europe should all be blown up or anything. It's just fun.

Royal descent is common among residents of the United States. It has been estimated that probably as many as 150 million Americans (half of the population) have traceable royal European descent.[7] More than half of the Presidents of the United States (27 of 42) have had a traceable royal descent or a wife with a traceable royal descent.[8] According to American genealogist Gary Boyd Roberts, an expert on royal descent, most Americans with significant New England Yankee, Mid-Atlantic Quaker, or Southern Planter ancestry are descended from medieval kings, especially those of England, Scotland, and France. Some Americans may have royal descents through German immigrants who had an illegitimate descent from German royalty.[9]

Due to primogeniture, many colonists of high social status were younger children of English aristocratic families who came to America looking for land because, given their birth order, they could not inherit. Many of these immigrants maintained high standing where they settled. They could often claim royal descent through a female line or illegitimate descent. Many Americans descend from these 17th-century British colonists who had royal descent. There were at least 650 colonists with traceable royal ancestry[10][11], and 387 left descendants in America (almost always numbering many thousands, and some as many as one million).[10] These colonists with royal descent settled in every state, but a large majority lived in Massachusetts or Virginia.[10] Several families, who settled in those states, over the two hundred years or more since the colonial land grants, interwinded their branches to the point that almost everyone was somehow related to everyone else. One writer observed, "like a tangle of fish hooks" [12].

Over time, opposing factors have affected the percentage of Americans who have provable royal descent. The passage of the generations has further intermingled the ancestry of the English colonists' descendants, thus increasing the percentage who descend from one of the immigrants with royal ancestry. At the same time, however, waves of post-colonial immigrants from other countries decreased the percentage who have royal descent.

The Medieval Genealogy Society sites this reference: Frequently Asked Questions for soc.genealogy.medieval

In The Royal Descents of 500 Immigrants, Roberts includes almost 350 colonial American immigrants with royal ancestry. These immigrants (pp. xiv, ff.):

"left sizable, often huge, progenies...These 350 are a large enough group so that living Americans with 50-100 colonial immigrant ancestors in New England (or Long Island), in Quaker (but not German or Scots-Irish) Pennsylvania, or in the Tidewater South (but often not the Piedmont, Shenandoah Valley, or mountainous 'backcountry') can expect to find a royally descended forebear."

Of these 350 immigrants, 167 left ten or more descendants treated in the Dictionary of American Biography. In the New England Historic Genealogical Society newsletter NEXUS, June-September 1994, Roberts says (p. 104) that 100 million is very likely quite a conservative estimate of the number of American descendants of these 167.