The Boston Marathon bombings cast a shadow Friday over the start of debate on legislation to remake the U.S. immigration system, as some Republicans argued that the role of two immigrant suspects raised questions about gaps in the system.

There was no suggestion that the two suspects, brothers who had lived in Dagestan neighboring Chechnya in southern Russia, had entered the U.S. illegally. And authors of a sweeping new immigration bill, which got its first hearing Friday before the Senate Judiciary Committee, argued that their legislation would improve U.S. national security because the estimated 11 million people now living here illegally would have to come forward and undergo background checks.

Still, a number of lawmakers seized on the events in Boston to raise questions about the existing immigration system and the changes proposed in the new bill. And there were concerns among supporters of the legislation that, even if it turns out that the bombing suspects did not violate U.S. immigration laws, the events could inflame anti-immigrant sentiment just as Congress confronts the already formidable task of getting a far-reaching immigration bill through the House and Senate and to the president’s desk.

“Given the events of this week, it’s important for us to understand the gaps and loopholes in our immigration system,” Sen. Chuck Grassley, R-Iowa, the Judiciary Committee’s senior Republican, said in his opening statement at Friday’s hearing. “How can we beef up security checks on people who wish to enter the United States? How do we ensure that people who wish to do us harm are not eligible for benefits under the immigration laws, including this new bill?”

Earlier in the week, Rep. Steve King, R-Iowa, told the National Review that Congress should be cautious on immigration in the wake of the bombings, focus on national security and put on hold any question of a path to legalization.

Supporters of the legislation disputed such arguments.

“I’d like to ask that all of us not jump to conclusions regarding the events in Boston or try to conflate those events with this legislation,” Sen. Chuck Schumer, D-N.Y., said at Friday’s hearing a few minutes after Grassley spoke.

“In general, we’re a safer country when law enforcement knows who is here,” and has photos and background checks, Schumer added — steps that would be taken in regard to people living here illegally under the legislation Schumer sponsored with seven other senators.

Republican Sens. John McCain of Arizona and Lindsey Graham of South Carolina released a statement decrying efforts to use the Boston events to stop the immigration push.

“Some have already suggested that the circumstances of this terrible tragedy are justification for delaying or stopping entirely the effort for comprehensive immigration reform. In fact the opposite is true,” McCain and Graham said. “Immigration reform will strengthen our nation’s security by helping us identify exactly who has entered our country and who has left — a basic function of government that our broken immigration system is incapable of accomplishing today.”

Republican Florida Sen. Marco Rubio’s spokesman, Alex Conant, said in a statement that “legitimate policy questions” could be asked about whether the immigration system played any role in what happened in Boston. But he added that “Americans will reject any attempt to tie the losers responsible for the attacks in Boston with the millions of law-abiding immigrants currently living in the U.S. and those hoping to immigrate here in the future.”