Can a tudung-wearing Muslim woman be such a symbol in multiracial Singapore?
Many people have a problem with this, which leads me to the second area she can make a difference: promoting Singapore's brand of multiracialism.
What is this brand?
It is about each race preserving its own distinctiveness and accepting the other's right to do so, but all sharing a common sense of belonging to the community.
This requires tolerance and understanding of one another's ways and of what the country's common interests are.
The balance isn't easy to achieve because if each race continues to build on its own distinctiveness, it can grow apart from the others.
For the Malay community, an overly strict adherence to eating halal food, for example, can reinforce its exclusiveness.
Similarly, if Chinese Singaporeans speak Mandarin even in the company of Malays or Indians, they weaken everyone's sense of belonging to the same community.
In fact, the very idea of race and its place in Singapore can make for a divisive society. Which is why it needs constant tending and vigilance, and deep understanding and empathy. Now, the multiracial idea is being placed under the brightest possible spotlight in the highest office of the land.
Will it shine even more brightly or suffer under the glare?
Having a tudung-wearing president can be a strong statement about the place of minority races in Singapore, that there is space for them and their beliefs and practices.
But it will require sensitive handling on her part because racial prejudices and stereotyping exist and her distinctiveness can work against her.
It will also be particularly challenging for President Halimah because of the controversy surrounding her election.
There is still much unhappiness on the ground and many remain opposed to the idea of a reserved election and the way it has been introduced.
The cynicism, if not addressed, can damage the office of the presidency and its occupant.
President Halimah will have her work cut out for her.
But when the challenge is great, there is opportunity to make a difference.
It was what motivated Singapore's first popularly elected president, the late Mr Ong Teng Cheong, to do what he did.
He too entered new waters, tasked with making the new office work. I believed the challenge shaped his approach and he was determined to show that he was his own man and that he would do whatever he thought necessary to do the job.
It led to several clashes with the Government but it helped shape the relationship between the two and deepened understanding of how to make it work better.
President Halimah's challenge is different: After three elected presidents, the formal role of safeguarding the country's reserves and overseeing key appointments has more or less been settled.
Less understood is the informal unifying role the president plays in multiracial Singapore.
President Halimah now has a unique opportunity to reinforce the importance of this part of her job under trying circumstances.
I hope she can turn adversity into advantage. If ever a unifying president is needed, now is the time.
•The writer is also a senior fellow at the S. Rajaratnam School of International Studies, Nanyang Technological University