With the global economic crisis continuing to bite, the US president-elect's calls to protect American jobs at all costs might also bring him into conflict with the Chinese government.
In his congratulations to Obama on Wednesday, Hu called for a closer US-China relationship which he said would be "for the benefit of Chinese and American people, and people around the world."
But he added that bilateral relations should still be conducted on the basis of the so-called "three communiques" - a reference to three documents that have formed the bases for ties since the US and China established diplomatic relations in the late 1970s.
One of main elements of the communiques is a US pledge to adhere to the so-called 'One China principle'.
At the core of that is the position that the US must not officially recognise an independent Taiwan, a self-ruled island that Beijing considers part of its territory, awaiting reunification.
Despite this, the US remains Taiwan's most important military backer and its biggest supplier of weapons – an issue that frequently irritates Beijing.
In his own congratulatory message to Obama on Wednesday, Taiwan's president, Ma Ying-jeou, said he too was looking forward to developing relations with the future US president.
"President Ma wishes to express his congratulations and appreciation for president-elect Obama's support for Taiwan-US ties and our China policy," a foreign ministry statement said.
"Taiwan hopes that its traditional friendship with the US will further develop under his distinguished leadership."