Feinstein told reporters that Tsarnaev could be interrogated now for any information on possible further terrorism threats under a public safety exception to immediately informing a suspect of Miranda rights.
"If he's not Mirandized, it can't be used in a court of law," she said, noting authorities already had "plenty of evidence" that can be used to convict him.
Suspects initially questioned under the public safety exemption and then later tried in civilian court include Umar Farouk Abdulmutallab, the "underwear bomber" who attempted to blow up a Detroit-bound airliner on Christmas Day in 2009, and Faisal Shahzad for his 2010 attempt to detonate a bomb in Times Square.
Conservative GOP Sen. Lindsey Graham of South Carolina made a similar argument to CNN in calling for Tsarnaev to be declared an enemy combatant for now, then later being criminally charged and put to trial in a civilian court.
According to Graham, a public safety exception to reading Miranda rights will expire, meaning the ability to continue interrogating Tsarnaev could be jeopardized by his right to remain silent and be represented by an attorney.
The public safety exception to the Miranda rule allows investigators to question suspects before apprising him of their rights when they believe there is an imminent public safety threat.
Despite Graham's warning that the exception will expire, Attorney General Eric Holder has opened the door to longer interrogations for that purpose in cases involving "operational" terrorists.
Another political dispute stemming from the Boston bombings involved calls by some conservative Republicans to put off consideration of bipartisan immigration reform legislation for now.
GOP Sen. Dan Coats of Indiana said Sunday that Congress should wait until the emotional reaction to the bombings subsides before tackling the volatile issue of immigration. His comment to ABC followed a similar call last week by fellow Republican Sen. Chuck Grassley of Iowa, who noted the Tsarnaev brothers were immigrants.
"It's important for us to understand the gaps and loopholes in our immigration system," Grassley said, asking "how can individuals evade authorities and plan such attacks on our soil?"
Schumer, one of the "Gang of Eight" senators who drafted the immigration plan, said some on the right who opposed the bill were using the Boston bombing as an excuse to stall the legislation.
"If they have a reason, a suggestion as to how to change it based on what happened in Boston, we'll certainly be open to it," Schumer said. "But we're not going to let them use what happened in Boston as an excuse, because our law toughens things up."
Graham, a Republican co-author, agreed it was time to tackle the immigration issue, saying "we need to move on."
Immigration reform resonates with the Hispanic-American community, which is the nation's fastest-growing demographic and heavily supported President Barack Obama's re-election last year.