After Columbus, English, Dutch and Portuguese fishermen, Basque whalers, and French fur traders all made visits to New England. The French even tried to set up a settlement. But at that time, the area was densely populated by highly civilized Native Americans. They weren't too excited about colonialism and rebuffed the French settlers. But then between 1616-1619, a mystery plague wiped out 75-90% of the native population, and that was after a hundred years of steady mortality from diseases spread by the Europeans.

Sailing along the Massachusetts coast in 1619, Captain Thomas Dermer described the impact on the region, noting that “ancient plantations, not long since populous, now [lay] utterly void; in other places a remnant remains, but not free of sickness.”

When the Mayflower expedition landed, they found deserted cities, fields planted with corn ready to harvest, and neat groves of trees. They attributed their good fortune to God and managed to survive the winter and continue building settlements.

“There hath, by God’s visitation, reigned a wonderful plague [that has resulted in] the utter destruction, devastation, and depopulation of that whole territory, so as there is not left … any that do claim or challenge any kind of interest therein. We, in our judgment, are persuaded and satisfied, that the appointed time is come in which Almighty God, in his great goodness and bounty towards us, and our people, hath thought fit and determined, that those large and goodly territories, deserted as it were by their natural inhabitants, should be possessed and enjoyed by such of our subjects.” – King James I, The Great Patent of New-England

http://www.cvltnation.com/the-great-dying-new-englands-coastal-plague-1616-1619/

A strong case was made for the mystery plague to have been caused by the spread of leptospirosis carried in rat urine, but it's still debated.

You may be looking specifically for answers regarding the current territory of the United States; however, if you expand this to include North America, there is a lot going on.

The Spanish conquered and expanded through Central and South America in the 16th century. After Cortés, one of the infamous conquistadors, conquered the Aztec Empire (also known as the Triple Alliance), the Viceroyalty of New Spain was established. Spain extracted wealth from its colonies in the form of both precious metals and natural resources. Native inhabitants were forced to work for Spanish settlers through the encomienda system. Spain also colonized the islands of the Caribbean – Havana, Cuba and San Juan, Puerto Rico, were both founded in the 1500s. From New Spain, the Spanish launched expeditions north, venturing into what is now the American Southwest. Coronado’s 1539 expedition revealed no large empires threatening Spanish expansion, and Don Pedro de Peralta founded the city of Santa Fe in 1609.

In what is now Canada, Jacques Cartier explored around the St. Lawrence in the early 1500s, and claimed that territory for the Kingdom of France. Samuel de Champlain would go on to found permanent settlements in New France, but not until shortly after Jamestown was founded. Newfoundland was settled by the English in the early 1600s as well.

I’m not particularly knowledgeable about reasons preventing colonization of what would become the 13 Colonies, and later the United States, during this period, but I hope I was able to at least partially answer your question.

I'll be copying a few older posts of mine here, mostly covering a bunch of failed Spanish attempts to colonize what's now the United States.

In what's now the continental US (and elsewhere, but let's stick with the US for now), the first wave of colonists were vigorously resisted, which is why the likes of Juan Ponce de León, Pánfilo de Narváez, Lucas Vázquez de Ayllón, Hernando de Soto, Tristán de Luna , and Juan Pardo are best remembered for their failures to establish colonies in La Florida. Just to hit the highlights:

• In 1521, Ponce de León ran afoul of the Calusa's shoot-first-ask-questions-later policy regarding the Spanish (likely encouraged by the Taino refugees who established villages under the Calusa's protection after fleeing the Spanish invasion of Cuba). Fatally wounded, Ponce de León retreated from Florida and promptly died. He's rather charitably remembered as the man who led the European discovery of the mainland US, though his attempts to establish a permanent presence there failed.

• The same year that Ponce de León died, Lucas Vázquez de Ayllón was organizing efforts to colonize what's now the Carolinas from the Bahamas, a region that was known on Spanish maps in the 1520s as Tierra de Ayllón due to his royal charter on the territory. Men under Ayllón's command captured dozens of Native slaves from the area in order to establish guides, informants, and translators for the eventual colony. Ayllón's favorite was a man given the name Francisco de Chicora (Chicora being the name of his tribe). Chicora traveled with Ayllón to Spain to drum up support for the colony, and in 1526 the two of them, along with 600 others established San Miguel de Gualdape - the first European colony in the continental US. Chicora, now home, promptly abandoned the colony. After three months of dwindling food reserves and persistent indigenous resistance and slave rebellions, 150 surviving colonists fled back to the Bahamas. Ayllón was not among them.

• Two years later, Pánfilo de Narváez (the same guy who failed to arrest Cortez in Mexico) led another expedition into what's now Florida. Narváez's expedition bypassed the Calusa but was rebuffed by the Apalachee near modern Tallahassee, FL. Afterward, Narváez's ground forces attempted to retreat back to the naval forces on hastily crafted rafts. Narváez's raft was swept out to sea and the conquistador was never seen again. The others went along the Gulf coast until they were shipwrecked in near Galveston, TX. Of the 300 men who made landfall with Narváez, only 86 reached Texas and only four ever reached Spanish territory again. Álvar Núñez Cabeza de Vaca, who spent eight years in Texas before walking the long way to Mexico City, is the most famous of these survivors.

• Cabeza de Vaca's report of the American Southeast and Southwest inspired two more expeditions into the current US in the late 1530s through the early 1540s. Francisco Vázquez de Coronado led an expedition into the Southwest, eventually crossing into the Great Plains, guided by Cabeza de Vaca's fellow survivor Estevanico, who died during the Zuni resistance of Coronado. Unlike the other conquistadors here, Coronado had the good fortunate of making it out of his failed expedition alive, after reaching as far as Kansas or so.

• Unlike his contemporary, Hernando de Soto didn't know when to call it quits. Between 1539 and 1542, he marched his men from Florida to North Carolina, and from there westward across the Mississippi, guided in part by a member of Narváez's belated rescue party that had been stranded in Florida. Unlike Narváez, de Soto's men narrowly managed to defeat the Apalachee and secured Anhaica, the Apalachee's principal town, as their base of operations. However, the Apalachee carried out an extensive and successful guerrilla campaign against the Spanish, forcing them out of the town to follow faint hopes of green pastures elsewhere. From there, de Soto's expedition is a cascade of tragedy, for himself as well as the indigenous nations he contacted. He managed to survive for as long as he did based on a combination of dumb luck and paranoia that somehow managed to overcome his hubris and greed. His men kept advising him to pick this territory or that territory as his colony, but de Soto was always unsatisfied and kept leading his men onward in a war of attrition he was ultimately losing. Eventually, de Soto died of a fever on the western bank of the Mississippi. After a failed attempt to cross Texas to get back to Mexico, de Soto's men were forced to flee down the Mississippi pursued the vast armada of Quigualtam, whose forces boasted that they would conquer Spain if only they had ships to reach it. It seems that Quigualtam brandished his boastful armada as warning against future attempts at conquests, as they seemed more interested in harrying the Spanish and reclaiming Spanish-held captives than actually wiping out the exhausted expedition completely.