Necessity of compromise is one of the major components of democracy. Without compromise, practicing democracy is hardly possible. An example of how lack of compromise could affect governance is the incidence related to raising the United States' sovereign debt limit, which occurred in 2011.
Both Republicans and Democrats were at loggerheads without any compromise from any of the sides until the nearing of the deadline. Missing the deadline might have meant suspensions of salary and jobs for those in the military and government. Necessity of compromise involves the opposing political parties and the country's leader.
When the former U.S. President, James Madison drafted the U.S. Constitution, he hoped for a check and balance system of powers. This system requires the necessity of compromise between the government's executive, legislative and judicial branches.