Why were the republicans so intent on expanding the boundaries of the us, and why did the federalists oppose an expansionist program? What factors accounted for the Federalists inability to regain national power after they lost the election of 1800?
The issue of expansion was not as highly partisan as your question implies. There were many Democratic-Republians who had concerns about westward expansion and many Federalists who strongly supported it.
But generally speaking, farmers living on the western frontiers tended to support the Democratic Republicans. Therefore, that party was growing in strength as more western States joined the Union, while the Federalist party dwindled. The Federalist party was focused primarily in New England, which was more focused on trade with Europe and building a manufacturing sector. The Democratic-Republicans were more focused on farming and agriculture, which was the primary economic activity of the new western communities.
It was actually the Federalists, and later the Whig Party that succeeded them, that supported building canals and later railroads that helped cement the connections between the east coast States and the western frontier.
As far as Federalist loss of power, Alexander Hamilton was really the head of the party and responsible for its organization. After the Vice President killed him, the Party did not really have a successor to lead the party. President John Adams was favorable to Federalist policies, but never considered himself a member of the party. John Marshall was probably the most prominent Federalist, but his role as Chief Justice kept him out of electoral politics.
Federalists were simply too focused on policy and not on developing a political base of voters. Their economic policies were largely seen as benefiting wealthy commercial and financial interests, at the expense of the common man. Thus, as voting expanded to include much of the poorer and working class people, Federalist support dwindled. Many party leaders thought working class people would naturally vote for the commercial and social leaders in their communities, but this was not the case.
I hope this helps!