In this atmosphere, referendum opponents say it's hard to run an effective campaign.
The referendum on constitutional change would abolish the post of Prime Minister, allowing the President to appoint cabinet ministers and bring all state bureaucracy under his control.
Presidential and legislative elections would be held at the same time.
Erdogan's advisor Sukru Karatepe was accused this week of suggesting in an Ankara publication that, if approved, the changes could lead to a federal system in the country but the government said his comments were misunderstood.
Erdogan's supporters argue that a "yes" vote would enable the president to speed up policy implementation that's normally complicated by Parliament.
At a rally in Istanbul, one of four he held in the last hours before Sunday's vote, Erdogan described the constitutional proposals as the biggest change in Turkey since the country was established almost a century ago, and the culmination of the response to July's abortive putsch. The military has contributed to Turkey's democratic deficit.
The referendum comes amid troubled times for Turkey, which has been plagued by a string of bombings, renewed violence between the government forces and Kurdish rebels and a failed coup attempt in July that resulted in a state of emergency that remains in place. Upon becoming prime minister in 2003, Erdogan managed to place civilian oversight over military expenditures and gutted the generals' hold on the National Security Council. In 2010, Erdogan's government took several hundred officers to court on charges of planning to overthrow the government.More news: North Korea displays new missiles in military parade
Ahead of the vote, United Nations experts accused Turkey of "massive violations" of the right to education and work, citing figures suggesting that since the state of emergency was declared, some 134,000 public servants had been dismissed.
They say his ability to retain ties to a political party - Mr Erdogan could resume leadership of the AK Party (AKP) he co-founded - would end any chance of presidential impartiality.
The one concern of Osman, an Erdogan supporter at another rally in Gaziosmanpasa, is that the president once had an alliance with the US -based preacher Fethullah Gulen, now his arch-enemy and blamed for the coup. Turkey's once-booming economy has stalled as terror attacks drove away tourists and unemployment climbed to seven-year highs.
The president would have a five-year tenure, for a maximum of two terms. More than 40,000 people, including opposition pro-Kurdish legislators, have been arrested.
The outcome Sunday is unclear, with some polls showing the country divided, and the main uncertainty is whether voters are telling the pollsters their true intentions Sunday or whether they've made up their minds. Last month, he lashed out at Germany for using "Nazi tactics" and called the Dutch "fascists" and "Nazi remnants" for blocking efforts to campaign for the referendum in the Netherlands. Also noticeable, the many posters supporting the Turkish President and the "Yes" campaign granting broad new powers.
Utko Cakirozer, a former editor of the opposition daily Cumhuriyet, who's now one of six parliament members from Eskisehir, had gone to the "In Heavy Demand" coffee house to cheer on the "no" campaign.
The OSCE Office for Democratic Institutions and Human Rights conducted the limited referendum campaigning observation mission in Turkey at the invitation of the country's authorities.