Prime Minister Malcolm Turnbull says the changes are aimed at empowering voters and ending so-called backroom preference deals.
But Labor has accused the government of rushing through the changes without allowing enough time for public consultation.
It's the most significant reform to Senate voting in more than 30 years.
Constitutional law expert George Williams, at the University New South Wales, says it is important to get it right.
"I think this Bill should be passed - we do need to reform the Senate voting system. But before it is passed the bill needs o be fixed. In particular, the Bill does not give voters the choice between candidates, and it gives too much power to the major parties to themselves determine which candidates are elected."
The changes abolish controversial group voting tickets which critics say mean parties, rather than voters, decide who gets elected into the Senate through so-called preference deals.
Under the reform, voters will be asked to number at least six boxes above the line, but people who number just one box will still have their vote counted.
The vote would then be exhausted and not flow on to other parties.
Professor Williams says this system - known as optional preferential voting - should also apply below the line.
Currently, voters need to number the boxes for each individual candidate when voting below the line.
In 2013, this meant numbering from 1 to 110 in New South Wales - and 1 to 97 in Victoria.
Professor Williams says the change is truly what's needed to ensure voters have a real say at the polls.
"Having a voting system that requires someone to sequentially number up to 110 boxes is not a system people are going to be disposed to use. And it creates a very major disincentive for people who may really want to vote for candidates. That is really not acceptable. And the result is to place very great power in political parties to themselves determine who gets elected at a party level, and you lock out voters in making a choice they would otherwise be disposed to make."
A fiery debate in the Senate had politicians from the major and minor parties both accusing each other of self-interest.
Finance Minister Mathias Cormann introduced the bill into the Senate, saying he wants the package debated in the middle of this week.
A half-day public hearing is scheduled for Tuesday before a parliamentary committee reports on the reforms later this week.
Labor senator Stephen Conroy says the government's timetable is denying Australians the chance to have their say on the changes.
"The majority of Australians who might have an interest in this issue are being denied an opportunity to put forward their point of view. They're being denied an opportunity to attend and participate as a witness and then we're going to have it rammed through with a report next week."
Senator Cormann rejected the accusation.
"That is completely false. That has never been the government's intention. The government's intention always has been to commence the debate this week. So our intention would be for the debate to continue and certainly to continue into the subsequent sitting week, which I believe is the week of the 15th of March."
Greens leader Richard Di Natale says an inquiry into 2013 election has already canvassed the issues, and Labor's call for a longer inquiry is unnecessary.
"They [Labor] don't support the legislation. So what they're doing is that they're hiding behind process, like cowards. It's all about the process. The truth is they don't support giving back power to the voters. They don't support it."
Family First senator Bob Day says the bill will wipe out the much needed voices of minor parties, and he won't be backing the reform.
"You need independent people who don't toe a party line in this place. Independents play a vital role in this place. I accept that on my own I am a nobody in this place, however as one of 79 minor parties and independents who ran at the last election, we will not take this lying down."
The electoral matters committee is due to report back to parliament on March 2.
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