An initial effort to present the change in a private members Bill by Nakifuma County MP Robert Kafeero earlier this year was dismissed by some as a joke but was sufficient to set in motion a debate that has pervaded the country now for months.
Speaker of Parliament Rebecca Kadaga poured cold water on Mr Kafeero's effort when she ruled in July that the debate was unmerited at the time.
A special aide to the president, Mr David Mafabi, has been the public face of mobilisation for lifting of the age limit, presiding over seminars in various parts of the country to popularise the move.
If successful, this will be the second major change to Uganda’s 20-year-old Constitution to directly favour President Museveni’s continued stay in power.
In 2005, an amendment was passed to remove term limits at a time when President Museveni’s tenure had ended after two elective terms.
Mr Museveni first shot his way to power in 1986 after a five-year guerrilla war, and ran the country unelected for 10 years before presenting himself as a civilian in the 1996 elections under the individual merit movement system.
In 2006, President Museveni returned now as candidate for the National Resistance Movement, which had been registered as a political party after the lifting of the ban on parties.
Apart from 1996, all previous elections that President Museveni has won with comfortable margins, have been disputed as rigged and fraught with other malpractices.
The Supreme Court has upheld three of those elections, ruling that the existence of irregularities did not affect, in a substantial manner, the final outcome which it said largely reflected the will of the people.