Mr Somchai is a softly spoken former judge - but also related to Mr Thaksin
Thailand's governing People's Power Party has named Somchai Wongsawat as its candidate for prime minister to succeed Samak Sundaravej.
The softly spoken former judge is a brother-in-law of the controversial former PM, Thaksin Shinawatra.
But within hours of the announcement a powerful faction within the ruling party said it would not support him.
Correspondents say the PPP has two days to reach consensus or risk renewed political instability.
A state of emergency was lifted in Bangkok on Sunday, 12 days after it was imposed amid violent clashes between government supporters and opponents, which left one person dead.
But anti-government protesters have vowed to continue their nearly three-week-old occupation of the main government complex until the PPP is forced out of power altogether.
Parliament is scheduled to vote on the PPP's nomination for prime minister on Wednesday after it became clear that the former incumbent, Mr Samak, would be unable to muster enough support to make a fresh bid for the post.
Over the weekend executives from the PPP underwent long negotiations with the party's coalition partners to win their support for Mr Somchai and on Monday it appeared they had achieved consensus.
Mr Somchai, 61, is married to Mr Thaksin's sister - but in other respects the former judge and career bureaucrat was thought to be viewed as an acceptable compromise candidate.
But Mr Somchai's candidacy was swiftly rejected by leaders of the People's Alliance for Democracy (PAD), the protest group which triggered the current crisis.
Like Mr Samak before him, they complain that Mr Somchai would be beholden to Mr Thaksin - now in exile but facing charges of corruption relating to his five years in office.
And within hours of their announcement of Mr Somchai's selection, dozens of members of the PPP said they would not vote for him.
"We are prepared to choose a candidate who will not aggravate problems already faced by the country," said faction spokesman Banchong Wongtrairat, according to Reuters news agency.
The rebel lawmakers have reportedly rejoined PPP talks over the leadership but the BBC's Jonathan Head in Bangkok says the ruling party is now badly divided over the issue.
He says that the PPP must find a new consensus. If it cannot, it risks breaking up into competing factions, a result that might please the government's opponents but would do little to restore political stability.