The Boston Marathon bombings ought to spur even swifter action on immigration reform, Sen. Lindsey O. Graham (R-S.C.) said Sunday.

"What happened in Boston ... I think should urge us to act quicker, not slower, when it comes to getting the 11 million [illegal immigrants living in the U.S.] identified," Graham said on CNN's "State of the Union."

Tamerlan and Dzhokhar Tsarnaev, the brothers suspected in the bombings, are of Chechen origin and immigrated to the United States in 2002.

Tamerlan Tsarnaev, left, and Dzhokhar Tsarnaev, the brothers suspected in the Boston Marathon bombings.

Graham is part of the bipartisan "Gang of Eight" senators who have unveiled a sweeping immigration reform proposal. At the Senate Judiciary Committee's first hearing on the proposal Friday, Sen. Charles E. Grassley (R-Iowa) urged his colleagues against rushing ahead on reform in light of the questions about the Boston Marathon bombings.

“While we don’t yet know the immigration status of the people who have terrorized the communities in Massachusetts, when we find out, it will help shed light on the weaknesses of our system,” Grassley said.

Sen. Daniel Coats (R-Ind.) said Sunday that he agrees with Grassley.

"We have a broken system, it needs to be reformed. But I'm afraid we'll rush to some judgments relative to immigration and how it's processed. So let's do it in a rational way rather than an emotional way," Coats said on  ABC News's "This Week With George Stephanopoulos."

Sen. Charles E. Schumer (D-N.Y), a second member of the Gang of Eight, on Sunday warned opponents of the immigration bill not to use the Boston bombings as a tactic for stonewalling the legislation.

"We are not going to let them use what happened in Boston as an excuse, because our law toughens things up," Schumer said on "State of the Union."