Updated

The Boston bombings and the foreign-born suspects have become part of the Capitol Hill debates on legislation to overhaul immigration law -- with critics of the proposal saying Sunday the terror attacks expose gaps in the country's system and supporters saying the tragedy could be a turning point in fixing a broken system.

“Now is the time to bring all of the 11 million (illegal immigrants) out of the shadows and find out who they are,” South Carolina Republican Sen. Lindsey Graham told CNN’s “State of the Union.”  “We may find some terrorists in our midst who have been hiding in the shadows.”

Graham and New York Democratic Sen. Chuck Schumer, members of a bipartisan Senate group working on immigration reform, said a key part of the legislation is better tracking of who enters and exits the United States on visas.

“The 19 (9/11) hijackers were all students who overstayed their visas and the system didn't capture that,” Graham argued. “We're going to fix that. … What happened in Boston should urge us to act quicker.”

Two bombs placed Monday near the Boston Marathon finish line killed three people and injured more than 180 others.

The first suspect, Tamerlan Tsarnaev, 26, was killed early Friday morning in a police shootout. His 19-year-old brother, Dzhokhar Tsarnaev, was captured by police that night and remains in the hospital.

Dzhokhar became a naturalized U.S. citizen last year. However, the Department of Homeland Security recently held up Tamerlan’s citizenship application after learning the FBI interviewed him in 2011 about possible ties to a militant group in Russia.

“Our law toughens things up,” Schumer told CNN. “There are some on the hard right, some otherwise, who oppose our immigration bill from the get-go, and they're using this as an excuse. We are not going to let them do that.”

He suggested the legislation, introduced last week and being debated in the Senate Judiciary Committee, could be amended in light of the Boston tragedy.

The bombing suspects-immigration debate essentially started when Iowa Republican Sen. Chuck Grassley said Friday during a Judiciary Committee hearing: "Given the events of this week, it’s important for us to understand the gaps and loopholes in our immigration system.”

Four key parts of the immigration bill are the improved Visa tracking, securing U.S. borders, improving the employee verification system known as E-Verify and providing a path to citizenship for some of the roughly 11 million illegal immigrants in the U.S.

New York Republican Rep. Peter King told “Fox News Sunday” that federal officials should ask tough questions of people wanting to live in the U.S. and coming from countries that are known hubs of terrorism.

“We should not be afraid to ask the extra questions,” he said.