"We will start to breathe again," one of Rousseff's foes, Senator Magno Malta, told reporters outside the senate, "and the doctor will say the nation has shown signs of life and will be stable soon."
If 41 of the country's 81 senators vote to impeach her, Rousseff would be served a written notice of the decision and forced to temporarily step down. Vice-President Michel Temer would assume the presidency.
Senators would have 180 days to conduct hearings ahead of a final vote to determine her fate.
According to unofficial tallies by Brazilian media, at least 50 senators are planning to vote for impeachment. The final margin will be closely watched as a barometer of support for her full removal.
A two-thirds majority of the Senate will be needed to permanently unseat her, so if at least 54 senators vote for impeachment today, it will be widely interpreted as a sign that her presidency is probably finished.
Rousseff is accused of improperly using loans from government banks to patch budget gaps and fund popular social programmes. Senators must decide whether this amounts to a "crime of responsibility" under Brazilian law.
Rousseff's opponents say she deceived legislators and the public about the state of the country's finances in order to conceal her mismanagement of the economy.
She denies any wrongdoing and insists that her predecessors used the same bookkeeping tactics.
At the Vatican, Pope Francis - the first Latin American Pontiff - expressed hope that Brazil will find unity after this "time of difficulty."
Rousseff narrowly won re-election in 2014, but recent polls show that her approval rating has slumped to about 10 per cent.
Attorney-General José Cardozo, who is defending Rousseff, said he would file additional appeals to the Supreme Court, but its justices have dismissed previous attempts to halt the process.
Protesters opposed to Rousseff's impeachment held street rallies and blocked roadways in at least 21 states yesterday. Rousseff and her leftist Workers' Party have rallied supporters by painting the push to oust her as a "coup" and a threat to Brazilian democracy, which was restored in 1985 after two decades of right-wing military rule. Rousseff, 68, was jailed and tortured by the dictatorship for her activities as a leftist militant.
Rousseff showed no sign of giving up in a speech yesterday.
"I am not tired of fighting," she said, criticising former political allies, such as Vice-President Temer, who have turned against her. "I am tired of those who are disloyal and traitors. I am sure Brazil is also tired [of them], and it is this fatigue which drives my fight every day."
Last month Brazil's Lower House voted 367 to 137 to impeach Rousseff. The interim house Speaker stunned the country on Tuesday when he tried to annul that vote, but he changed his mind less than 24 hours later, clearing a path for today's vote in the Senate.
