This paper develops a theory of wedge issue politics in modern democracies. It argues that wedge issues are associated with a politics of intransigence which differs from the politics of concessions that typically comes with non-wedge issues. This theory explains why Prime Minister Theresa May opted for a divisive approach to secure ratification of her Brexit agreement in the House of Commons. Due to the intra-partisan division within the Conservative Party, the government had an incentive to employ politics of intransigence. Playing a chicken game with recalcitrant party members, it relied on bargaining strategies to force party rebels to back down. This politics of intransigence further deepened intra-partisan divisions and thus prompted both sides to harden their stance. This vicious circle not only brought the Conservative Party to a breaking point but eventually led to government failure.