The White House has announced that Mr Obama will arrive next Thursday for a 24-hour visit before returning to the US to try to push his controversial domestic healthcare reforms onto the statute books.
The Federal Government hopes Parliament will sit for special sessions on Thursday and Friday, when Mr Obama will address Parliament before leaving the country.
But the popularity of the Masterpieces From Paris exhibition at the National Gallery means accommodation is booked out across the capital.
There is already little room for the thousands of staffers and politicians who flood into Canberra on sitting weeks.
Leader of the House Anthony Albanese says he is working on the logistics and will make an announcement soon.
Masterpieces From Paris is the largest and most valuable collection of art ever exhibited in Australia and features 112 paintings by artists including Vincent van Gogh, Paul Gauguin, Paul Cezanne and Claude Monet.
More than 300,000 people have already visited the exhibition, which was only expected to have 250,000 visitors in total.
Visitors, 80 per cent of whom have travelled from interstate, have queued for up to three hours to view the exhibition, which will be on show until April 18.
The priceless works are on loan from the Musee d’Orsay in Paris and it is the first time they have been brought together in an exhibition outside of France.
Seven van Goghs, nine Gauguins, eight Cezannes and five Monets are among the works showcasing the explosive arrival of modern art in Europe.