Henrique Eduardo Alves said a group of lawmakers has found there's not enough time to organize the plebiscite so its results could take effect during next year's presidential race, according to the state-run Agencia Brasil news agency.
Rousseff has said she wants the results to take effect during the October, 2014, elections, but under Brazilian law that means the plebiscite would have to be held no less than a year before the race.
A host of other top politicians, including Vice President Michel Temer, had already cast doubt on the feasibility of organizing a plebiscite before October, though Temer later backtracked.
Congressional party leaders also said Tuesday they would favor drafting political reform legislation and submitting it for a popular referendum instead of the plebiscite, which would allow citizens to vote yes or no to a series of proposals, with legislation to be drafted based on the results.
House leader Alves announced a working group would be created within 90 days to hammer out a proposal for political reform.
The head of Rousseff's Workers Party, Jose Guimaraes, said his party would work with only two parties that support the proposed plebiscite to collect the 171 signatures necessary to push the measure through.
"Congress is wrong in not wanting to discuss the plebiscite now," Agencia Brasil quoted Guimaraes as saying.
The demonstrations took off in June over a 10-cent hike in bus and subway fare in Sao Paulo and morphed into a mass, nationwide movement voicing public dissatisfaction with a range of issues such as high taxes and poor public services like education and health care. Government corruption and ineffectiveness were also among the protesters' top complaints.
In response, Rousseff floated a raft of proposals including $23 billion in new spending on urban transportation, using oil royalties to fund education, and importing thousands of foreign doctors to work in impoverished, underserved areas.
Along with pushing Congress to approve the plebiscite on political reform, she's also ordered her Cabinet to focus on and devise solutions for five priority areas: fiscal responsibility and controlling inflation, political reform, health care, public transport and education.