"It is likely that the banks have not fully acknowledged all the losses that they're going to experience ... and some banks won't make it," he said.
The move to push the Democrat-sponsored bill through the senate comes amid fresh reports that the global economy is in a worse state than previously predicted.
Hours after it began its passage, Chinese officials disclosed that about 20 million migrant workers had lost their jobs across the country as the world's third-biggest economy by gross domestic product struggles to deal with the slowdown.
"A large number of migrant workers from rural areas have lost their jobs and have income problems after going back to their home villages," Chen Xiwen, a rural employment director, said.
China has suffered a slump in its manufacturing output as the Asia-Pacific region suffers from the slowdown.
Australia on Tuesday unveiled a $26bn stimulus plan to counter the worst effects of the downturn on its economy.
The money would be spent on schools, housing and roads, with cash handouts going to low- and middle-income earners, the government said in a statement.
Philip Robertson, the director of the Asia Human Rights and Labour Advocates, said: "I think the stimulus plans will help the [global] economy in general, but what is clear ... [is that] migrants are the first to lose their jobs.
"The stimulus plans may be too late for migrant workers."
Kevin Rudd, the country's prime minister, acknowledged the country's budget will be plunged into a deficit as a result of the package.
In Japan, the country's central bank said that it would start buying up shares held by Japanese banks in an attempt to stimulate the country's economy.
In South Korea, exports shrank at their fastest rate ever in January, the government has announced.
Exports plunged by nearly 33 per cent in January compared to a year ago - the fastest decline since the country began recording such figures in the late 1950s.
Imports also fell by 32 per cent as South Korean consumers reined in spending.
The results follow the release of a report last week by the Geneva-based International Labour Organisation predicting that up to 230 million people around the world could be unemployed by the end of the coming year.