There are just five sittings days of both houses of the Federal Parliament scheduled next year before a possible election in May, leaving the government with few opportunities to pass high-profile legislation it promised ahead of the 2019 election.
Mr Morrison was on Tuesday asked if he could guarantee the passage of the contentious bills before next year's ballot, and if he was prepared to start the election campaign having not met the commitments.
But he dodged the questions, as he refuted suggestions that the Coalition had broken any promises.
He once again tried to blame Labor for the fact the government was yet introduce its federal integrity commission legislation, implying that it wouldn't take that step unless the opposition flipped its position and backed its heavily criticised model.
"We have said very plainly that we would like to take this through on a bipartisan basis," he said.
"Our model is not supported by the Labor party, who have a two-page proposal [for an integrity commission]. We have 349 pages of detailed legislation."
Mr Morrison offered a similar response when asked in question time if the stripped-back sitting calendar was evidence that he had "no intention" of trying to push through the legislation before the next election.
Labor used question time to try and expose the weaknesses in the government's integrity commission model, asking rhetorically if it would have the power to investigate scandals such as the dodgy documents saga involving Energy Minister Angus Taylor.
Communication Minister Paul Fletcher reiterated that the government's model would tackle allegations of serious criminal corruption at the federal level, as he challenged Labor to back its proposal if it was serious about the issue.
The Coalition earlier voted for the third time in a week to block debate on Helen Haines' integrity commission bill, following a fresh push from independent Rex Patrick on Tuesday afternoon.
The government is in a race against time if it wants to pass its signature religious discrimination bill, which was finally unveiled and introduced to the Federal Parliament last week.
While the government insists the laws will provide a "shield, not a sword" for people of faith, equality advocates fear it could open the door for discrimination against groups, including LGBTIQ people.
Labor's caucus agreed on Tuesday to hold off on setting a final position on the bill until after a parliamentary inquiry had been handed down, due in early February.
The timeframe and limitations of the inquiry are causing concern.
A coalition of advocacy groups say they've been "locked out" by the inquiry process, which will include just three public hearings in Canberra.
"Individuals from affected communities, particularly women, people with disability, LGBTIQ+ people and people of faith should be at the very heart of the parliamentary process established to consider the impacts of the bill," Equality Australia chief executive Anna Brown said.
"Instead, the government's timeline is locking us out."
The deputy chair of the committee conducting the inquiry, Labor's Graham Perrett, was concerned the probe was being conducted during religious events such as Hanukkah and Christmas.
"Many people, whether religious or not, will be focused on spending time with family rather than writing submissions for this inquiry," he said.
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