First things first, Thomas Jefferson isn't just rumored to have liked it... he did like it. As a matter of fact, macaroni and cheese was largely popularized in America by French Master Chef James Hemings' recipe, which he devised while learning French "cookery" with master chefs in France, and his was something one congressman called "pie of macaroni" after enjoying the dish in 1802 at the White House. The congressman, in truth, did not enjoy the dish but it continued to spread in popularity nonetheless. And in an odd coincidence, while that congressman dined inside with the President, a gigantic cheese wheel lay in the White House known simply as the Mammoth Cheese. It was gifted to President Jefferson from a town in Massachusetts through the Baptist congregation of Rev John Leland. How mammoth was it? At over 1,200lbs its rumored to have taken every cow in the area to provide the milk - being some 900 cows. So much milk was donated that three cheeses were made, the largest being selected to gift our chief executive. It was so big it lasted at least three years (delivered on New Year's Day 1802) and the nasty remnants were allegedly thrown into the Potomac River sometime in 1805, two years after maggots began to nibble on the block. They made it in a six foot cider press and even had the logo Rebellion to tyrants is obedience to God stamped into the surface, a motto which Ben Franklin proposed for the Great Seal of the United States but, failing to secure it for that purpose, it later was appropriated as a personal logo of Jefferson. Jefferson wrote of the cheese;

the Mammoth cheese is arrived here and is to be presented this day. it is 4 f 4½ I. diameter, 15. I. thick, and weighed in August 1230. ‚Ñî. They were offered 1000. D. in New York for the use of it 12. days as a shew.

Not wanting to appear improper in regards to reception of gifts as President, Jefferson paid Leland, who he had met when the Reverend resided in Virginia, 200$ for the cheese. Anyhow, Hemings' recipe was not the first in America as a cookbook available in many colonies was published in 1769 with a similar recipe (posted in the link below). The dish from which both recipes are derived is much, much older, and you can read about how it became modernized (up through colonial times) here, which includes some old recipes and even the mac and cheese recipe I use (trust me, it's amazing).

So what cheese did Jefferson have available? A lot of imported permesan as well as cheddar, a real American cheese though it did not originate here. For many colonial or early republic Americans importing parmesan wasn't really an option, so they bought local or, more commonly, made their own. How did that start? The epicenter of early cheese production was Rhode Island, Connecticut, and, as you may have guessed from the folks in Chesire making a block so large it needed a sleigh to transport it, Massachusetts. The practice crept west, and soon New York and Vermont became big time cheese producers. Once Ohio was opened to settlement they became the epicenter of cheese production and remained so until the mid 1800s (when Wisconsin took over and still is our cheese capital to this day). We know there was cheese in the Mayflower when the Pilgrims landed and pretty much since that time cheese production has happened in the colonies/states.

Cows give a lot of milk and you can't just turn them off or not milk them until you need to - your cows required milking daily from spring through fall (they did not produce during winter months in colonial America). What could you do with all this milk besides drink/cook it or give it away? There were two options to stabilize it and greatly increase its shelf life; make cheese and/or make butter. The Pilgrims brought both on Mayflower and soonafter the early Puritan settlers came with both the knowledge of cheese production and plenty of cows needed to supply the commodity. How? The (raw) milk is heated, something like rennet (an animal byproduct, vinegar or leman/citrus could also be used) is added, and the mixture is then left to seperate. Once the curd separates the mix was poured over cheesecloth to allow the liquids/whey to run through (which was usually collected and used for other dishes). Bam, just that easily you've essentially got cottage cheese. Want a more refined product? Well, you gotta get more of the remaining whey out, so the cloth would be wrapped around the curds and then squeezed, slowly forcing the whey out. Or hung by a string and left to drip out. By whatever process the whey would be extracted, drying and increasing the flavor of the cheese. To really make a refined cheese this would be placed into a press (either a screw press or a weight press) and held under pressure for a while, forcing most of the remaining whey and moisture out of the curd and pressing it into a firm block. Put that on a shelf for a while to allow those enzymes to do their thing, flipping and salting rather often, and now you have a genuine "farmers cheese." Not content with such a simple product, many New England farmers further refined their cheese by "melting" the curds together and removing even more whey in a process they brought from England to make cheddar which was quite stable, meaning it could be carried to market and sold rather easily. These were the two most common refined cheeses in America pre-1800 by far and most colonists, particularly those proximal to cows, goats, or sheep, would have been exposed to at least farmers cheese from one of these animals' milk.

Curds, the primary building block that makes cheese, were also used in a variety of recipes and were likely the most common type of "cheese" consumed in British North American colonies and, later, American States. We see in Mary Randolph's 1824 cookbook recipes for Curds and Cream, as well as a Curd Pudding. She also lays out a recipe for rennet;

TO PREPARE RENNET.

Take the stomach from the calf as soon as it is killed--do not wash it, but hang it in a dry cool place for four or five days; then turn it inside out, slip off all the curd nicely with the hand, fill it with a little saltpetre mixed with the quantity of salt necessary, and lay it in a small stone pot, pour over it a small tea-spoonful of vinegar, and sprinkle a handful of salt over it, cover it closely and keep it for use. You must not wash it--that would weaken the gastric juice, and injure the rennet. After it has been salted six or eight weeks, cut off a piece four or five inches long, put it in a large mustard bottle, or any vessel that will hold about a pint and a half; put on it five gills of cold water, and two gills of rose brandy--stop it very close, and shake it when you are going to use it: a table-spoonful of this is sufficient for a quart of milk. It must be prepared in very cool weather, and if well done, will keep more than a year.

As you can see, cheese was a very labor intensive process. But Randolph, who was the sister of Thomas Mann Randolph, husband of Martha "Patsy" Jefferson, wasn't the first to publish such recipes in America. In 1769 a cookbook by Elizabeth Raffald was published in England and spread to the colonial printshops across the Atlantic. It had numerous recipes involving curds or cheese, such as;

To make Cheese-Cake.

SET a quart of new milk near the fire, with a spoonful of rennet, let the milk be blood warm, when it is broke, drain the curd through a coarse cloth, now and then break the curd gently with your fingers, rub into the curd a quarter of a pound of butter, a quarter of a pound of sugar a nutmeg, and two Naples biscuits grated, the yolks, of four, eggs, and the white of one egg one ounce of almonds well beat, with two spoonfuls of rose water, and two of sack, clean six ounces of currants very well, put them into your curd, and mix them all well together

To make Curd Puffs.

TAKE two quarts of milk, put a little run- net in it, when it is broke, put it in a coarse cloth to drain, then rub the curd through a hair sieve with four ounces of butter beat, ten ounces of bread, half a nutmeg, and a lemon peel grated, a spoonful of wine, and sugar to your taste, rub your cups with butter, and bake them a little more than half an hour

Or;

To make a Ramequin of Cheese.

TAKE some old Chediire cheese, a lump of butter, and the yolk of a hard boiled egg, and beat it very well together in a marble mor- tar, spread it on some dices of bread toasted and buttered; hold a salamander over them, and send them up

It is also Raffald's recipe for Macaroni and Parmesan Cheese in this book that is generally credited as the first modern macaroni and cheese recipe.