Fresh allegations against Sonia Gandhi's son-in-law Robert Vadra and communal violence in Kishtwar are threatening the second week, which has just three working days.
The view within the government is that normalcy will be restored in Parliament only by August 21, when the two Houses will resume after a six day break beginning from August 15.
The government is expected to propose to the Opposition parties that the parliament can sit on two Saturdays - August 24 and 31 - to make up for lost time, and then the session could be concluded on time.
"There is a broad consensus on the food security bill and we are hopeful that all parties will like to discuss it in detail," said a senior minister.
The government managers also point out that all political parties will be interested in passing the bills to amend the Right to Information Act to keep themselves out of it, and also the bills to reverse the Supreme Court judgments disqualifying convicted MPs/MLAs and banning those in jails from contesting elections.
READ: 35 MPs want political parties in RTI ambitREAD: Pawar raises pitch for changes in food security billREAD: BJP will not oppose Food Security Bill in Parliament: Rajnath