What problems did colonists face in Plymouth?

The Plymouth settlers faced a number of serious problems upon arrival in the New World. For one thing, they were the victims of bad timing. They arrived in winter and so were unable to do much in the way of planting crops to harvest. Instead, they had to rely on the limited food supplies they'd brought with them on the Mayflower. These supplies soon ran out, leading to hunger and starvation.
The winter weather also made it impossible to establish any kind of shelter on land. Once again, the settlers had to remain on board ship instead of venturing outside. The harsher the conditions, the longer it would take to get any kind of settlement up and running.
In addition to all the other challenges, the Plymouth colonists were forced to endure outbreaks of serious illness and disease, such as scurvy. Without a supply of fresh fruit containing Vitamin C, the settlers were vulnerable to this potentially fatal disease.