Barack Obama says he expects a "difficult few days"
The EU and Canada have warned that a clause in the US economic recovery package could promote protectionism.
The "Buy American" clause seeks to ensure that only US iron, steel and manufactured goods are used in construction work funded by the bill.
The EU ambassador in Washington said that if approved, the measure would set a "dangerous precedent".
The $800bn (£567bn) rescue plan package is under discussion in the US Senate this week.
Meanwhile, President Barack Obama is expected to name Republican Senator Judd Gregg as commerce secretary.
Mr Gregg would be the second member of the Republicans in Mr Obama's cabinet.
The president's first choice for the post, New Mexico Governor Bill Richardson, withdrew following questions about his links to big business.
The BBC's Jonathan Beale in Washington says Mr Obama will hope that Mr Gregg's nomination can help him secure approval for the stimulus package.
It is unlikely that the package, which has already been approved by the House of Representatives, will be able to pass the Senate without Republican support.
The White House has said it is reviewing the "Buy American" part of the stimulus bill, although Vice President Joe Biden said last week that it was legitimate to have some portion of Buy American in the final measure.
Mr Obama's signals as a presidential candidate on the campaign trail last year that he could rip up the North America free trade agreement were seen as a political gesture to win round the sceptical white working class vote, says our Washington correspondent.
Perhaps that has become more important with the economic crisis, but it leaves one wondering where the Obama administration really stands on free trade, he adds.
EU Ambassador John Bruton said that if passed, the measure could sap global public confidence.
"If we have a series of protectionist measures introduced, then the possibility of real global leadership is put at risk," he said.
"We regard this legislation as setting a very dangerous precedent at a time when the world is facing a global economic crisis."
In a letter to Senate leaders, the Canadian ambassador in Washington, Michael Wilson, said that if "Buy American" was in the final legislation, it would set a negative precedent with global repercussions.
"The United States will lose the moral authority to pressure others not to introduce protectionist policies," he wrote.
Canadian International Trade Minister Stockwell Day said Canada hoped to be exempted from any such measure, which he warned could lead to a global depression.
"These protectionist measures, in a time of recession, only make things worse," he told broadcaster CBC.
"It can only trigger retaliatory action and we don't want to go there."
There is also opposition from some senior US Republicans who say the measure could start trade wars.
Mr Obama has urged the US Congress not to delay his stimulus plan over modest differences.
He said on Monday that he was expecting a "difficult next few days" as the Senate debated the package.
He also warned that more US banks are likely to fail as the full extent of their losses in the economic crisis becomes clear.
The Democrat leader in the Senate, Harry Reid, has said he hopes the stimulus can be approved by the end of the week.