Both governments understood the importance of the healthcare bill and Obama's wish to see it through, Gibbs said, adding that the visits would be rescheduled for June.
A Yudhoyono spokesperson said the Indonesian president "had a feeling about this" and after reading the situation "it's proven to be true".
"The president can of course understand because we have monitored the situation in Washington DC," Dino Patti Djalal, a spokesman, told reporters.
"We can see how tight the political process is regarding the health reform bill."
"The delay of President Obama's visit to Indonesia is related to urgent internal matters, so we understand. Health reform has become a hot issue in the US"
Julian Pasha, Indonesian presidential spokesman
Dino Patti Djalal said under the circumstances Yudhoyono believed that it would be better for Obama to visit in June when he would be more relaxed.
Earlier this month scores of students took to the streets in the Indonesian capital and other major cities to protest against Obama's scheduled visit to the country, carrying banners branding him an enemy of Islam and an imperialist.
Julian Pasha, a presidential spokesman, said the authorities had made "maximum preparations" to boost security in Jakarta ahead of the visit.
"... but that does not mean we should be disappointed by the delay," Julian Pasha told the Reuters news agency.
"The delay of President Obama's visit to Indonesia is related to urgent internal matters, so we understand. Health reform has become a hot issue in the US."
The regional trip was intended to build on Obama's debut Asia tour last November, when he called himself America's "first Pacific president".
Obama's first stop was to have been the US territory of Guam, a US military base in the Pacific, before heading to Indonesia, the world's most populous Muslim nation.
The US president spent four years as a child in Indonesia where he was to try to build on his outreach to the Muslim world, and later visit Australia.