These are the names of the sons of Israel, who came into Egypt with Yaakov, each coming with his household: Reuben, Simeon, Levi, and Judah; Issachar, Zebulun, and Benjamin; Dan and Naphtali, Gad and Asher. (1:1-4)
An interesting discussion of this paragraph can be found here. Meanwhile, R' Amnon Bazak presents a rather incompatible understanding in this week's Shabbat Beshabbato.
[Pharaoh] said to his nation: "Behold, the nation of the descendants of Israel is too numerous and powerful for us." (1:9)
This is the first time Israel is referred to as a nation, not just as a family or collection of individuals. Perhaps there is a reason for the change in language beyond the simple numerical growth of Yaakov's descendants. Just two words before this word, we find a reference to another nation, the Egyptian nation. The juxtaposition of the two nations in the text may hint to a deeper meaning.
It may be that Pharoah felt threatened by the Jewish growth, but the people were less worried. If there was a war in the ancient world, one could expect the losing king and his dynasty to be defeated and exterminated, but from the perspective of the average peasant not much would change. Perhaps taxes would go up a little, or down a little, but as long as the disruption of war ended it didn't matter too much who ended up winning. Thus Pharoah himself must have felt threatened by increased Jewish power (which presumably would lead to demands for the same authority the Jews had in Yosef's lifetime), but the common people would have less reason to worry.
Pharoah's comment may have been intended to frame the brewing conflict, not in terms of a royal struggle for power, but specifically in terms of a threat to the Egyptian nation. As he presented it, the Jews were a pernicious cancer within the Egyptian people. The destinies of the Egyptian and Jewish peoples were mutually exclusive, only the fittest would survive, and it was the average Egyptian's job to protect himself from the enemy which, in some vague way, was supposed to threaten him and his people. Pharoah was the thus first social Darwinist and the first Nazi. If his ultimate aims were to protect himself and his rule, he nevertheless tried to convince the entire people that the real threat was towards them.
Pharoah's specific fear is that "when war approaches, [Israel] will gather with our enemies, fight against us, and rise up from the land". This last, cryptic, phrase can be explained in a way that supports the previous hypothesis. The Jewish lived in "the land of Goshen", which was part of the Nile delta and thus the lowest part of Egypt. By "rise up from the land", Pharoah may have meant the Jews would leave Goshen and take over the entire country. ("Land" would refer to Goshen, not Egypt as a whole.) Whether or not this threat was realistic, it was what Pharaoh wanted the people to believe. And Pharoah's use of the word "nation" regarding Israel, accentuated by the Sefer Shemot's adjacent reference to the "nation" of Egypt, hints that he exploited this possibility in his propaganda.