Actually, the original European settlers didn't come here illegally. There were no immigration laws set at that time. As for stealing the land, that's true of damn near every country in the western hemisphere. The age of colonizations was all about might makes right. What do you say we open up all the borders over here and bring back that way of life, but with our modern weapon technologies. That would be a great idea, yeh!
In fact the earliest settlers came to North America very legally. They were given charters by their governments to come to North America and setup shop. It's hard to get on a boat bound for North America without notice. There weren't that many of them.
The Pilgrims did not steal Indian land. Plymouth colony had generally excellent relations with the Indian groups in their area for the first 50 years or so. They allied with the Wampanoags during this time. The Wampanoags were in the midst of war themselves with the Narragansett who were forcing the Wampanoag to pay tribute to them. The Micmac had also just defeated the Penobscot and were threatening the territories of the Wampanoags. On top of that, the Wampanoags had been devastated by disease which had caused them to lose about 3/4 of their population. At the time of the Pilgrim arrival, the Wampanoag were in dire straits. It was not lost on the Wampanoag that the Pilgrims, with their superior weapons, would make excellent allies. The Pilgrims supported the Wampanoag in their renewed war against the Narragansett, who were themselves fighting the Pequot and, later, the Mohawk. The Narragansett, though weakened by these wars, tried to attack the Wampanoag again in 1632. Again the Pilgrims defended the Wampanoag and the Narragansett were defeated.
After that, things went downhill. After the death of Massasoit in 1661, his eldest son, known as Alexander to the English, took over the tribe but had very different ideas about the settlers than his father. Perhaps he was more savvy, perhaps more prescient. He realized that huge influx of English colonists, who by now far outnumbered the original Pilgrims, weren't so keen on cooperation so much as taking land from the already small territories of the Wampanoag who numbered only about 1,000 people due to repeated epidemics. On the pretext of inviting Alexander to peace talks, the colonists poisoned him and he died. Following that, Alexander's younger brother, known as Philip, took over the tribe. Philip rallied the other tribes in upper New England including their former enemies, the Narragansett.
In 1675, an Anglicized Indian, John Sassamon, who was a Harvard graduate and adviser to King Philip, was murdered by a group of Wampanoag when they discovered that he had warned the English colonists about King Philip's plans to attack the colonists. His murderers were tried and executed by the English and this made the Wampanoag furious as they felt this trial was a breach of their sovereignty.
What happened next was the single bloodiest conflict in the entirety of white American, and likely Indian, history. King Philip's war was short but it was brutal. Indians throughout the region banded together. England sent no military help. At the time the war started there were about 52,000 whites in New England. Somewhere between 600-800 of them were killed, including 1 out of every 10 direct combatants. Indian war parties massacred entire towns including women and children. Measured by percentage, that's worse than the Civil War. Whole towns were completely leveled and when the damage was assessed after the war, 12 towns were found to be destroyed along with 1,200 head of cattle.
As bad as this was, the Indians fared far worse. Over 3,000 Indians were killed but many more were sold into slavery, executed, or deported to Bermuda where their descendants remain to this day.
It was a lost cause. Since the time of the arrival of the whites, enormously devastating plagues of disease swept the Indian nations every few years, reducing their population in New England by about 75% by the time King Philip's War had started. With the attendant loss of resources, the average 3% per annum growth of the colonies, and what few white allies they had before the war started, there was no chance. Of course disease honors no treaties or borders and for the Indians, who had no natural immunity to the exotic diseases the whites unintentionally brought with them, more epidemics were to come further reducing their numbers.
There's a ridiculous myth that the American Indians lived in a sort of idyllic Eden prior to the arrival of the white settlers. People tend think they all lived in complete harmony with each other and that just isn't the case. There was actually quite a large Indian war in New England just before the Pilgrims' arrival. Like peoples everywhere else, they fought over territories and rights. It's naive and not a little patronizing to think that Indians were any less scrupulous about each tribe enhancing their own prospects in the world at large. Indians in other areas were no different. The infamous Aztec empire was the Rome of southern North America. They derived their power from conquering and slaughtering everyone else around them, those that survived they turned into slave states to serve Aztec interests.
I offer this not as a defense of European actions in the Western Hemisphere, but as a reminder that wars and interactions between cultures are far more complicated than they appear at a cursory glance. To this day, the single greatest factor in the decimation of the Indian population was not war, but diseases unwittingly brought by the European settlers who, at the time, had no idea how or where diseases spread or even what caused them. Even in the areas where whites and Indians had cordial relations, disease ravaged Indian populations. The earliest successful eastern settlers, the Pilgrims and their Strangers, were myopic people who did not understand Indian cultures at all. The Indians were the same. When the Naragansett sent a package of arrows to the Plymouth colony as a declaration of war, the Plymouth colonists thought this was a trade offering and sent back gunpowder and bullets. The Naragansett had no idea what this meant.
Each culture may as well have been Sonny Corleone opening the package with Luca Brasi's bulletproof vest wrapped around a fish. "What the hell is this??"
Careful when throwing around the term, "murderer." That accusation can be used by both Indians and whites in relation to the other.