Which group believed a strong national government was critical to the country?

federalists

anti-federalists

The federalists were the ones who wanted a strong central government

The US government was initially very weak under the Articles of Confederation .. They couldn't tax the states and thus had no money, couldn't enforce laws, had no central leadership, no standing army or courts, and whatnot. The Federalists were for strengthening the central government, and would eventually help draft documents to bolster power.