Lawmakers have debated whether the Boston Marathon attack justifies slowing the immigration bill’s passage, but a recent poll raises the possibility that the attack dealt a blow to the bill’s proponents, as almost half of Americans think legal immigration increases the nation’s vulnerability to terrorism.

“As a result of LEGAL immigration into the United States, do you think the threat of terrorism against the United States has increased, decreased, or stayed the same?” CBS and The New York Times asked last week. Forty-nine percent of Americans said that legal immigration “increased” the threat of terrorism, compared to 41 who said in decreased.

The poll was conducted between April 24 and April 28, after Sen. Rand Paul, R-Ky., told Senate leadership that the immigration bill should go on hold in light of the Boston attacks.

“We should not proceed until we understand the specific failures of our immigration system,” Paul wrote on the 22nd. “Why did the current system allow two individuals to immigrate to the United States from the Chechen Republic in Russia, an area known as a hotbed of Islamic extremism, who then committed acts of terrorism?”

Sen. Mike Lee, R-Utah, disagreed, though he opposes the bill. “In some ways, what happened in Boston this week is yet another reason to examine our immigration system,” Lee said at the Heritage Foundation.

Sen. Chuck Schumer, D-N.Y., who helped the author the bill as a member of the Gang of Eight, argued that “what happened in Boston and international terrorism I think should urge us to act quicker, not slower, when it comes to getting the 11 million identified.”

It’s not clear that such a counter-argument resonates with Americans — just 4 percent of respondents told CBS/The New York Times that legal immigration has caused the threat of terrorism to decrease.

This isn’t to say that immigration policy contributed to the Boston attacks, but rather that senators who raise the possibility are tapping into a broad-based sentiment that may strengthen their criticism of the Gang of Eight’s proposal.

“[T]his bill would allow the Secretary to overlook convictions for crimes related to gang activity, child abuse, domestic violence, and drunk driving in determining whether an individual is eligible for admission to the country if the person’s admission serves ‘humanitarian purposes,’ ‘ensure[s] family unity,’ or is in the ‘public interest,’” says a fact sheet on the bill from the office of Sen. Jeff Sessions, R-Ala. “These standards are so broad as to render most current legal restrictions meaningless.”