If petitions on the parliamentary website secure 100,000 signatures, the British MPs are obliged to hold a debate on the subjects raised.
Now the date of the debate is set to be released in the coming days.
The petition accuses Cameron of harming the poorest in society since he took office in 2010.
"The current Tory government has caused devastation for the poorest in society for the last five years. We cannot afford another five years of Tory rule, with the recent welfare reform that will cause nothing but immense poverty in the UK,” it reads.
Most of the opposition to Cameron comes from years of government’s austerity policies.
In 2010, Cameron’s government scrapped Education Maintenance Allowance (EMA), a weekly £30 grant for 16-18 year old students from poor households in England.
A survey carried out by the Association of Colleges in 2011 found there were nearly 50 percent fewer students in college because they "could not afford” to attend.
A recent YouGov poll found that Labour Party leader Jeremy Corbyn is one of Britain’s most popular public figures while Cameron is the most hated.