Local media report there was strong opposition to military intervention at a session of the upper chamber of parliament, the Senate, on Saturday, despite the fact that it is controlled by Mr Tinubu's party.
This was especially the case among lawmakers representing states along the more than 1,500km (930 mile)-long border with Niger, but there has also been countrywide condemnation of the possibility of war.
West African regional bloc Ecowas had set a deadline of Sunday for the junta to give up power - or face possible military action.
The decision was very much seen as Mr Tinubu's as he is Ecowas' current chairman, and Nigeria is its most influential member.
Although the junta has defied the ultimatum, Ecowas did not respond by immediately sending troops. This came as a relief to many Nigerians who prefer a diplomatic resolution to the crisis.
Some question whether a seven-day deadline was realistic given that Nigeria and other countries have to get parliamentary approval before deploying the military.
Many people are also appalled that electricity to Niger was cut on President Tinubu's orders, causing blackouts in Niger's capital, Niamey, and other cities.
Critics claim that this is in violation of a treaty that had enabled Nigeria to build a dam on the River Niger, though Mr Tinubu's supporters say the power cuts are aimed at pressuring the junta to hand back power to ousted President Mohamed Bazoum, without military confrontation.
Nigeria and Niger share strong ethnic, economic and cultural ties and any military intervention against Niger would affect northern Nigeria, already facing serious security challenges of its own.
An influential group of Muslim clerics in northern Nigeria said Mr Tinubu must not "rush into an avoidable conflict with a neighbour at the behest of global politicking".
