Some lawmakers called for a medical team to be formed to determine Chavez's state. Some also questioned why the letter was signed by the vice president rather than Chavez himself.
"Who's governing Venezuela? In Venezuela, Havana is governing, and that's the problem we have," opposition congressman Julio Borges said during the debate.
Barboza said that if Chavez's allies continue with their stance, the opposition will be forced to "convoke the people of Venezuela to re-establish the validity of the constitution." He didn't elaborate.
As he announced lawmakers' approval, Cabello said: "President Chavez, this honorable assembly grants you all the time you need to tend to your illness."
Legal experts have joined politicians in debating whether the inauguration can legally be postponed.
Constitutional law expert Henrique Sanchez Falcon, a professor at Central University of Venezuela, called the government's position "something that's absolutely contrary to what's established under the constitution, which says that the term lasts six years."
Maduro has called the swearing-in a "formality" and said the opposition is erroneously interpreting the constitution. Chavez has said that if he's unable to continue on as president, Maduro should take his place and run in an election to replace him.
Capriles noted, however, that Maduro "wasn't elected" to continue leading a government in Chavez's absence into a new term. "If Maduro wants to be president, it's not through that way," Capriles said.
He added Tuesday that he has spoken with members of the military, and that they have told him "we are with the constitution."
"The Armed Force also has a role to play to play here ... of respecting the constitution," Capriles said, without elaborating, while using the military's formal name.
Cabello said in an interview with Telesur that he's sure the military wouldn't join with the opposition. Later Tuesday night, state television showed a video conference between Maduro and top military officers in which Defense Minister Diego Molero said the military remains unified.
"You have a united, cohesive Bolivarian National Armed Force with very high morale ... and in addition to that, with unquestionable loyalty," Molero told the vice president. "We're committed heart, mind and soul to this revolutionary process."
Jorge Rodriguez, a Caracas district mayor and campaign manager in recent elections, accused the opposition of fomenting a "conspiracy" against Chavez's government. He insisted that Chavez remains president despite his health problems and pointed out that the National Assembly had granted the president permission to travel to Cuba for his operation.
The government had said on Monday that Chavez was in a "stable situation" in a Cuban hospital receiving treatment due to a severe respiratory infection. The government says he's coping with "respiratory deficiency," but hasn't said how severe it is.
Government officials called for Chavez's supporters to gather at the presidential palace on Thursday, and said some Latin American heads of state plan to attend.
The governments of Bolivian President Evo Morales and Uruguayan President Jose Mujica announced that the leaders would travel to Caracas.
Capriles urged Latin American leaders not to visit, asking them to instead demand that the Venezuelan Constitution be upheld. He said presidents of other countries such as Argentina, Brazil and Colombia should also take such a stance.
The opposition leader said he won't call for protests on inauguration day.
"What I won't do is put people to fight against people. Don't count on us," Capriles told reporters. "Our country doesn't need hate. Our country doesn't need fights."
Opposition coalition leader Ramon Guillermo Aveledo wrote to Organization of American States Secretary-General Jose Miguel Insulza on Monday explaining the opposition's concerns. Aveledo said in the letter that if Chavez doesn't appear on inauguration day and there is no declaration of a temporary absence of the president, "a serious violation of the constitutional order will have been committed."