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Mr. Graham, meanwhile, argued that the administration’s handling of the Benghazi attack was just the start of a pattern of bad management that also can be seen in the aftermath of the Boston bombings.

Democrats, including Mr. Obama, have defended the administration’s handling of the war on terrorism generally, by pointing to the death of Osama bin Laden and, joined by some Republicans, are cautioning against politicizing the Boston bombings.

Several lawmakers have defended the FBI and the U.S. intelligence community for not doing more to chase down intelligence chatter from Russia about the two suspects, both Chechen Muslims, prior to the bombings. They note that the Kremlin did not respond to several entreaties from U.S. law enforcement for more information about the Tsarnaevs and note that Moscow has its own political reasons for exaggerating Chechens’ ties to terrorism.

But Mr. Graham appeared eager to suggest that the White House’s overall posture toward the threat of terrorism has not been serious enough and that, as a result, the administration has fostered a law enforcement and intelligence environment susceptible to missteps and failures.

• Jerry Seper and Susan Crabtree contributed to this report.