President Obama’s fruitless three-year search for compromise with the Republicans ended in a thunderclap of a speech on Tuesday, as he denounced the party and its presidential candidates for cruelty and extremism. He accused his opponents of imposing on the country a “radical vision” that “is antithetical to our entire history as a land of opportunity.”

Mitt Romney, the Republican presidential front-runner, has embraced a House budget plan that is little more than “thinly veiled social Darwinism,” the president said, a “Trojan horse” disguised as deficit reduction that would hurt middle- and lower-income Americans.

“By gutting the very things we need to grow an economy that’s built to last — education and training, research and development, our infrastructure — it is a prescription for decline,” he said, speaking to a group of Associated Press editors and reporters in Washington.

Mr. Obama has, in recent months, urged Republicans to put aside their destructive agenda. But, in this speech, he finally conceded that the party has demonstrated no interest in the values of compromise and realism. Even Ronald Reagan, who raised taxes in multiple budget deals, “could not get through a Republican primary today,” Mr. Obama said. While Democrats have repeatedly shown a willingness to cut entitlements and have agreed to trillions in domestic spending cuts, he said, Republicans won’t agree to any tax increases and, in fact, want to shower the rich with even more tax cuts.