Here are the top 10 points in this developing story:
Earlier today sources said the Congress had almost settled on Sukhjinder Randhawa as the new Chief Minister but some MLAs had expressed reservations. A meeting of the Congress' legislature body - scheduled for this morning - was postponed to 1 pm and has now been further delayed as the party gathers opinions on Mr Randhawa's suitability.
Mr Randhawa - who earlier praised Mr Singh, calling him "our senior" and declaring he had always treated him "like my father" told news agency ANI: "Till now no name has been selected. Party observers have talked to all MLAs... Now a consensus will be made. Till it is announced, I will not react to anything."
This morning's meeting of the Congress Legislature Party was postponed after Rajya Sabha MP Ambika Soni - believed to be the party's first choice - declined the offer. Ms Soni said "no" at a late-night meeting with Rahul Gandhi; she stressed on the "ramifications" of a non-Sikh Chief Minister, particularly with an election due.
If it is held today, the CLP meeting will be the second in two days. Aware of its precarious position (and of the BJP, AAP and Akalis waiting to pounce), the Congress has worked swiftly but cautiously this weekend, and is keen to ensure the new Chief Minister has maximum internal support. Sources had said the CLP will be called only after all party MLAs are consulted.
Rajasthan Chief Minister Ashok Gehlot - who earlier this year narrowly survived instability in his government - has requested Mr Singh to "keep the interest of the party above all else." In a lengthy statement issued this morning, Mr Gehlot called on his colleague to "to rise above ourselves and think in the interest of the party and the country".
Months of sniping and hostility between Amarinder Singh and Navjot Sidhu came to a head late Friday after a sudden meeting of Congress MLAs. Sources told NDTV around 50 of the party's 80 MLAs wrote to Sonia Gandhi and asked for Mr Singh to be replaced.
A furious Mr Singh then spoke to Mrs Gandhi and told her he had had enough. "I was humiliated three times by Congress leadership..." he said. He wrote to Mrs Gandhi declaring himself "anguished" and to defend his administration's track record.
The Captain also told NDTV that though he had resigned, "... for the sake of my country, I'll oppose his (Navjot Sidhu) name for Chief Minister. It's a matter of national security... is an incompetent man... a total disaster..." Of further worry for the Congress, perhaps, was Mr Singh's response to staying with the party; "I can't answer right now."
The Singh-Sidhu feud dates to the 2017 election; Mr Sidhu had hoped to be Deputy Chief Minister but was reportedly denied by Mr Singh. He was instead made a minister but quit two years later. After a sulk he re-emerged, targeting Mr Singh and becoming a hard-to-ignore problem, forcing the party into a mediation attempt that soured after Mr Singh voiced disapproval at Mr Sidhu being made Punjab Congress chief.
The rift escalated sharply in recent weeks and a tenuous truce unravelled after statements by Mr Sidhu's advisers. Last month, four ministers and around 24 MLAs raised fresh complaints against Mr Singh, setting the stage for the weekend's drama.
With input from ANI