WASHINGTON—President Barack Obama sought to increase pressure on Congressional Republicans by attempting to hold them responsible if talks to prevent the so-called fiscal cliff collapse.

Mr. Obama, in an appearance on NBC's "Meet the Press," which was taped Saturday, cast himself as a reasonable broker prepared to make concessions, while depicting GOP leaders as unwilling to let taxes rise on the wealthiest Americans. Many in the GOP make the opposite case, blaming the budget impasse on Democrats, who are blocking any change...