The court, known as the TSE, could in theory scrap the results of the election, forcing either a snap election or for Congress to pick a new interim leader.
The court, known as the TSE, could in theory scrap the results of the election, forcing either a snap election or for Congress to pick a new interim leader in Latin America's biggest country.
This would be a bombshell for a country already wallowing in two years of recession and the fallout from the massive "Car Wash" corruption investigation.
Analysts say there is little chance of this, however, with Temer likely to keep his seat until regularly scheduled polls at the end of 2018.
The issue dates back to 2014 when Temer was vice president on the winning ticket of leftist Dilma Rousseff's reelection to the presidency. Last year, Rousseff was removed in an impeachment vote and Temer took over the top job.
Temer and Rousseff are now accused -- as are swaths of other politicians caught up in the Car Wash probe -- of taking undeclared campaign funds or bribes from corrupt donors. The TSE's job is to rule on whether the election was fatally compromised.
Both Temer and his former partner on the presidential ticket deny any wrongdoing.
Deliberations were to begin Tuesday and end on Thursday.
Brazilian media report that the judge overseeing the case, Herman Benjamin, will recommend that the full panel impose sanctions against Rousseff and Temer, with new elections.
However, Temer's center-right PMDB party and allied parties control Congress and they have the backing of big business. Following the Rousseff impeachment, there is little appetite for yet another abrupt change of president just when economic reforms are underway.
One way of kicking the can down the road would be if defense lawyers succeed in asking for more time to answer the case. A judge on the court may also decide he needs more time to study the huge quantity of evidence.
Another option is that the court could decide that Rousseff and Temer did take illegal donations but that the evidence does not support annulling their victory. It is also possible that the court will rule to scrap Rousseff's victory, while finding Temer not guilty and able to carry on.
"There's total calm. The president has time on his side, because there are many legal options," said a government source, who asked not to be named.
Since he took over, Temer has been plagued by rock-bottom approval ratings and a wave of corruption allegations against his close allies.
Despite his unpopularity, Temer says he will push through far-reaching austerity reforms to fix the broken budget and serve out the rest of Rousseff's original term until 2018.