Utpal Parrikar is being rumoured to be the BJP's candidate from Panaji, where by-election is slated on May 19.
The Christian holy day comes just days ahead of April 23, when the state will have polls for two Lok Sabha seats and bypolls for three Assembly constituencies.
The special session of the House was convened by Governor Mridula Sinha to conduct the floor test, after Sawant was sworn in as the CM during wee hours of Tuesday.
Assembly Speaker Pramod Sawant said names have been finalised for the North Goa and South Goa seats, but refused to reveal who they were.
The Mandrem bypoll will be held on April 23 and Sopte is almost certain to be fielded from there by the BJP.
His illness has also cast a shadow of uncertainty over the fragile ruling coalition in the coastal state, which is headed by the BJP.
In a Facebook post, the Congress president alleged that the attack was masterminded by the BJP's central leaders.
Goa Forward Party chief and Agriculture Minister Vijai Sardesai has hinted on the administration weakening ever since the Goa Cm has been hospitalised.
BJP Goa general secretary Sadanand Tanavade refused to divulge details in connection with the cyber attack.
The remarks were made by state Shiv Sena President Jitesh Kamat after he met Goa Governor Mridula Sinha demanding the dismissal of the BJP-led coalition government and dissolution of assembly.