In a university lecture today my lecturer claimed that if there had been a war between indigenous tribes and European forces the indigenous tribes would have stood a good chance.
He justified this claim by saying that North America had a bigger population, they had more developed agriculture, and that guns wouldn't have been a big advantage as they weren't actually deadlier, just easier to use.
These claims struck me as suspicious, but I'm always happy to learn more on the subject.
While this sort of view will always be somewhat speculative, your lecture probably has a good argument. European advantages were minimal at the onset of colonisation, and Native American's had numerous advantages of their own, including shorter supply lines and knowledge of the terrain. 1491: New Revelations of the Americas before Columbus by Charles C. Mann (a journalist, but his work is well respected by historians), gives a good overview of this period. Europeans (including the British and the French) has tried to settle North America several times before 1609, and mostly failed. Native people continually drove off these early attempts at settlement. Even after settlements were built (such as Jamestown and Plymouth) they were still vulnerable. The Powhatan Confederacy held off the colonists for 30 years, and under Opchanacanough destroyed about 1/3 of the Virginia Colony. King Philip's War in New England also did considerable damage, and initially looked like they might destroy the northern Colonies. It is also worth pointing out that many of these early colonies were hugely dependent on Native Americans for labour and subsistence, and so they were quite vulnerable.
The biggest weakness of the Indigenous people is that they were divided, and so were never able to form a united front, although many tried. The Powhatan's war against the British was undermined by other nations giving maize to the British. Philip's New England war was similarly undermined by British political manoeuvrings which succeeded in turning other Native groups against the Wampanoag. Critically, New York Governor Edmond Andros convinced the Mohawk to attack Philip's troops while they were negotiating, killing almost 500 Wampanoag warriors.
In addition, losses from disease made the diverse Native groups more casualty averse, and so they were much quicker to compromise, retreat, and negotiate, than they otherwise would have been, and this allowed the British and others some breathing space even when defeated. It also made it much harder for the Native people to defend their territory, or maintain warriors in the field. In general, these factors prevented Native Americans from committing their full force against the European invaders. This doesn't necessarily mean they would have won, but they were probably much closer to victory than history has traditionally recorded.