By Charles Haviland
BBC News, Islamabad
Some argue that Mr Zardari is not the right man for the job
The party of the assassinated Pakistani politician, Benazir Bhutto, is pushing hard for her widower, Asif Ali Zardari, to become the country's next president.
This comes in the wake of Monday's resignation of General Pervez Musharraf from the post.
But Mr Zardari is a controversial figure not acceptable to everybody.
The Pakistan People's Party (PPP), fiefdom of the Bhutto-Zardari family is the biggest in the country and is expected to make a decision by Friday.
That will be just before members of the fractious governing coalition resume their talks on the issue.
But most of the daily papers are quoting party sources as saying all of Mr Zardari's senior colleagues want him in the post.
The new government must address the problem of violence in the tribal areas
He has also won the support of the MQM, a party powerful in his own home province of Sindh.
Its leader said Mr Zardari deserved the job partly because of what he called his late wife's sacrifice for democracy.
The rise of the controversial Mr Zardari is testimony to the continuing power of dynastic politics in South Asia.
But his main coalition partner, the Pakistan Muslim League-Nawaz (PML-N) of his wife's long time rival Nawaz Sharif, may not back him.
It is thought to want a candidate from one of the two smaller provinces for the presidential post, which may have less power than it did under Mr Musharraf.
It is important for the coalition to make a deal so that attention can be focused on the continuing violence on the Afghan border, scene of a Taleban insurgency.
There are fresh reports of violence in the tribal areas on a daily basis.
One report said six people died when missiles from inside Afghanistan hit the compound of an elder, reportedly frequented by foreign militants including Arabs.