Both former cricketer Khan, and the cleric Tahir ul-Qadri, who runs a network of Islamic schools and charities, have called for PM Sharif to quit, accusing him of corruption and ballot-rigging during his landslide election victory last year.
Thankfully for Mr Sharif, Mr Khan and Mr Qadri were unable to muster the numbers they had hoped for in their march last week from the eastern city of Lahore.
But they still managed to mobilise tens of thousands of supporters, whose occupation of the capital represents a serious security risk for a country as volatile as Pakistan.
"As a goodwill gesture the government has decided to form two different committees to negotiate," Interior Minister Chaudhry Nisar said on Sunday.
Mr Khan's representatives did not respond to calls on Monday seeking comment on the government's offer. But a representative of Mr Qadri said the cleric rejected it outright.
"Dr Qadri will not speak to any of the committees. Our demand is simply that the government should step down," spokesman Shahid Mursaleen said.
Whereas the mass agitation has reinforced concerns over the fragility of democracy in the nuclear armed, insurgency plagued Muslim state, the country's powerful military has stayed out of the political fray so far.
Pakistan's overworked conspiracy theorists believe Mr Khan and Mr Qadri mounted their parallel protest campaigns because they sensed Sharif's fraught relationship with his generals had nosedived in recent months. Sharif's last term ended in a coup in 1999, and since taking office last year he has clashed with the military on several issues.
The current crop of generals are unhappy that Pervez Musharraf, the army chief who ousted Sharif before becoming president himself, is being tried for treason.
They also distrust Mr Sharif's dovish stance toward rival India, and were frustrated by his prevarications over the launch of military operations against Pakistani Taliban militants in tribal lands bordering Afghanistan.
But while the generals want a free rein over security and strategic matters, analysts doubt whether they want to overturn another democratically-elected government.
Police estimated the number of people participating in the two protests on Sunday at around 55,000, but the numbers wax and wane, with participants seeking shade from the baking sun in the middle of the day, and many spend the night at the homes of friends rather than camp out in the open.
Their occupation of two of the capital's main thoroughfares has, however, disrupted access to the heavily guarded "Red Zone", where the presidency, the parliament, the main government ministries, the country's top courts and most foreign embassies are located.
On Monday, however, traffic into the high security area was moving more easily.
Mursaleen said Mr Qadri's supporters - who came equipped with food, water tankers, and sleeping mats - would not budge, A Reuters journalist estimated the clerics supporters numbered up to 20,000.
The government's offer of talks followed a call from Khan on Sunday for his supporters not to pay taxes or utility bills. His appeal met with widespread ridicule since most Pakistanis who can get away without paying taxes and utility bills already do so - a major contributor to the country's economic woes.
In a veiled threat, Mr Khan also warned that he may not be able to stop his supporters from marching on parliament and the fortified enclave where most foreign embassies are located.
Such a move would be a recipe for violence given the heavy deployment of riot police and paramilitary forces.
On Monday morning, most newspapers published critical editorials of Khan and his Pakistan Tehreek-e-Insaaf party.
"Were Mr Khan's threats not so risible they would be worthy of the severest condemnation," said Dawn, one of the country's most respected papers.