Boston Mayor Thomas Menino said Sunday on ABC's "Face the Nation" that FBI agents might never be able to interrogate Tsarnaev because he was so seriously wounded in a shootout prior to his capture.
"We don't know if we'll ever be able to question the individual," Menino said.
Republican Sen. Dan Coates, R-Ind., a member of the Senate Intelligence Committee, echoed Menino's concerns.
"The information that we have is that there was a shot to the throat," Coates said. "It doesn't mean he can't communicate, but right now I think he's in a condition where we can't get any information from him at all."
"He is in no condition to be interrogated at this point in time," added Boston Police Commissioner Ed Davis on "Fox News Sunday."
Meanwhile, the FBI said Sunday Tsarnaev was in "serious" condition.
"According to Beth Israel Deaconess Medical Center, Dzhokhar Tsarnaev remains in serious condition," the FBI said in a statement. "The FBI is releasing this information at the request of the hospital."
Tsarnaev is accused of setting off the two backpack bombs that caused three deaths and injured dozens during the Boston Marathon last week and then allegedly gunned down a university police officer before being was arrested. His older brother, Tamerlane, was killed in a gun battle Thursday night.
The federal government was expected to charge 19-year-old Dzhokar with terrorism as early as Sunday, sources told CNN.
Precisely how that happens remains a subject of debate. Tsarnaev could be charged criminally or held as an enemy combatant who could be interrogated by intelligence officers without being represented by an attorney -- assuming he's capable of speaking at some point.
Menino he hoped the U.S. government would "throw the book" at the accused marathon bomber.
"I hope that the U.S. attorney, Carmen Ortiz, takes him on the federal side and throws the book at him," he said. "These two individuals held this whole city hostage for five days. That's what these terrorist events want to do, hold the city hostage and stop the economy of the city."
Davis, the Boston police commissioner, said the inquiry into Monday's bombing remains complex and as new evidence comes to light it may impact what charges are levied.
"We are examining every possibility here," Davis said. "We have told the people of Boston we feel that they're safe at this point in time, and we continue to say that. There may be other components to this investigation that will lead to charges down the road. This is a very intensive and wide-ranging inquiry."
The fallout from Friday's arrest didn't stop at the debate over how to prosecute the suspect, though. Two Republican lawmakers urged the shelving of immigration reform during the inquiry along with greater scrutiny of the American Muslim community.
Rep. Peter King, R-N.Y., said Sunday the FBI should intensify its efforts to ferret out radical Muslim terrorists who may be living in the United States. Coates, the Indiana Republican, said he favored holding off on immigration legislation until more is learned about the two natives of Chechnya who were accused of planting the deadly bombings.
King and Coats were among the members of Congress who called Sunday for a close look at the potential reasons the Tsarnaev brothers were apparently not under law-enforcement scrutiny despite a lengthy visit Tamerlan Tsarnaev made to Russia and Dagestan in 2011.
Although a solid connection to Chechen militants has not yet been established, King said on "Fox News Sunday" the bombing pointed out the U.S. war on radical Islamist terrorism was not over and law enforcement need to keep developing information within the Muslim community in the United States. "If you know a certain threat is coming from a certain community, that's where you have to look," said King, who added that "99 percent of Muslims (in the United States) are outstanding Americans."
Coats, a member of the Senate Intelligence Committee, told ABC's "This Week" the Boston investigation had a greater sense of urgency than immigration reform and reform should be put on hold until the dust settled.
"Immigration is an issue that has dramatic economic effect on Americans. It also has national security implications," Coats said.
The House Intelligence Committee Chairman, Rep. Mike Rodgers, R-Mich., defended the FBI's handling of the case. Agents interviewed one of the suspects after a foreign government asked for information, believing Tamerlan Tsarnaev had become radicalized.
Rodger said on NBC's "Meet the Press" he thought the FBI had been "very prudent and very thorough" in its handling of the initial Tsarnaev interview.
The FBI was continuing its investigation when the foreign government that first gave U.S. agents the tip stopped cooperating, Rodgers said.
"[The FBI] asked for more help from that intelligence service to try to get further clarification and unfortunately, that intelligence service stopped cooperating," he said. "So what happens is that case gets closed down."