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The Federalist feared the Louisiana Purchase because they believed that it would upset the balance of power when the new territories would be settled and later apply for statehood to the Union.  Once accepted as a state the Federalists were afraid that these new states would snatch their political influence in government.  Others thought it would undermine the powers of the state since it was not put to a vote which also undermines the power of the Federalist government.  This was not acceptable to them.