The above response is incorrect. John Smith did not marry Pocahontas; in fact the entire story of her "saving his life" was greatly embellished by Smith many years later.
The colony did have many problems, primarily because those who came were more interested in searching for gold than survival techniques. There was an uneasy alliance with the local Indians who provided some food willingly; and Smith's strict rules (he who does not work shall not eat) helped the colony get past its first winter. However, Smith was injured in a gunpowder explosion and was forced to return to England for medical treatment. Once he left, the colonists reverted to their old ways and risked starvation again; in fact they were ready to abandon the colony, but while sailing up the James River they met a vessel containing Lord De la Warr, and many supplies. Also arriving was Sir Thomas Gates the new governor who imposed a new system of governance known as the Lawes Divine and Martial. The Lawes were harsh, but did allow the colony to survive.
Economic survival was indeed the result of tobacco production; but it was John Rolfe who introduced it. Rolfe managed to breed a variety of tobaccos and produce a milder variety that was popular in Europe. Rolfe married Pocahontas in a political marriage, and later took her to England where she died. Rolfe himself was killed in a war with the Indians when greedy colonists reneged on agreements with the Indians and begin stealing Indian land and crops.
The colony of Jamestown, like several other English colonies prior to it almost perished as well. Landing in 1607, the lack of food brought about starvation, lack of sanitation brought about dysentery, and the lack of diplomacy with the Natives brought about warfare.
Part of the problem with the food supply was due to the fact that many of the colonists were "Gentlemen Farmers" from England looking to enlarge their estates, not necessarily do the hard work of farming. When they could no longer barter for food with the Natives, they stole it, causing armed conflict.
However, John Smith (1580-1631) assumed control in 1609 and brought about a truce, partially the result of his marrying Pocahontas, and the colony survived. It began to finally thrive in 1614 when it found the right commodity, in the form of tobacco, to export to England at a profit.