Whether it was 2 years or 200 years, the academic consensus was that it was incredibly fast. I would likely lean more toward the longer time-frame, as the archaeological record is more consistent with a "slower" migration. Stuart Fiedel gives the mainstream account of a migration that took around 100-150 years.
The Thule culture, which is ancestral to recent Inuit or Eskimo
groups, developed on the west coast of Alaska and spread by a swift
coastal migration from northern Alaska to Greenland and Labrador
(McGhee 1984). Thule people traversed this distance of about 1,500 to
2,000 miles in less than 150 years, between A.D. 900 and 1050 (fig.
He continues by pointing out one of the difficulties in accepting an even more rapid migration - it left residual communities along the way. In fact, he contrasts this later in the paper to the seemingly more rapid movement of the Clovis population southward into the areas around present day New Mexico, and notes the lack of intermediary settlement as one of the substantiating reasons.
The main point to be emphasized here is the rapidity of movement in each case.
Thule people covered more than 1,500 miles in
100 to 150 years, sloughing off sufficient populations along the
migration route to fill the intervening territory and to create a
visible archaeological record.2
By the most direct route, Clovis ancestors would have covered about
1,300 miles travelling from Alberta to New Mexico. They could have
done this in less than 100 years. In fact, they previously may have
trekked through the ice-free corridor in a matter of months, leaving
no archaeological record (but see Mandryk, this volume).3
Beyond that, the consensus is currently diverging if not on the speed of the Thule migration, but on the time. This illustrates the difficulty in establishing anything beyond a rough estimate. One of the main driving factors behind this re-examination has been deeper and more rigorous examination of the achaeological sites, as explained by Ramsden and Rankin.
In recent years there have been even further assaults on the accepted
Thule radiocarbon chronology. Over the past 20 years, the accumulation
of many more radiocarbon dates has inevitably led to more anomalies,
in addition to more precision. The new spate of activity has included
the luxuries both of redating known samples, and of dating new samples
from sites whose age had previously been attested by one sample only.
Some results have been quite startling. Where a larger series of dates
have been run on a site from which only one date was available before,
the original date has sometimes turned out to be anomalous and quite
divergent from the new series.4
To further complicate matters, archaeology isn't the only tool for tracking population movements. Bellwood offers linguistic changes in the region as another piece of evidence that supports incredibly rapid movement.
The entire migration from Alaska to Greenland perhaps took only a few
decades, reflecting the vast distances between exploitable resources
in the landscape. What was the stimulus? Archaeologists variously
suggest that the movement was encouraged by a desire for Greenland
iron, hunting or caribou and musk oxen, and by the mobility required
to hunt Arctic bowhead whales. As Michael Fortescue (2013: 340) notes,
the migration was rapid enough to be traceable through linguistic
studies alone: "In fact, the Thule migrations from North Alaska as far
as East Greenland about a thousand years ago represent a paradigm case
for the rapid expansion of a language into virtually uninhabited
regions, with ensuing gradation of innovations and losses away from
its original homeland."5
So, in short - a single lifetime? Possibly. Many generations? Possibly. The consensus is that it was noteworthy for its speed, but the details are elusive.
1 Fiedel, Stuart J. "Rapid Migrations by Arctic Hunting Peoples" in The Settlement of the American Continents: A Multidisciplinary Approach to Human Biogeography, Barton, C. Michael, editor. p79
2 Ibid. p79-80
3 Ibid. p80
4 Ramsden, Peter and Rankin, Lisa. "Thule Radiocarbon Chronology and Its Implications for Early Inuit-European Interaction in Labrador" in Exploring Atlantic Transitions: Archaeologies of Transience and Permanence in New Found Lands, Pope, Peter Edward and Lewis-Simpson, Shannon, editors. p302
5 Bellwood, Peter. First Migrants: Ancient Migration in Global Perspective. p108