WASHINGTON  Debating an overhaul of the health care system, the Senate found itself tied in knots on Thursday over a bipartisan proposal to allow people to import lower-cost prescription drugs from Canada and certain other countries.

Democratic leaders delayed a vote, in part, because they feared that the proposal would be approved, potentially blowing apart a deal negotiated by the White House and the pharmaceutical industry.

The industry, represented by the Pharmaceutical Research and Manufacturers of America, or PhRMA, adamantly opposes legalizing additional imports and says the government could not guarantee the safety of imported medicines.

As members of Congress before last year’s election, President Obama and his chief of staff, Rahm Emanuel, supported efforts to allow drug imports. But now the Obama administration, like pharmaceutical companies and the Bush administration, is raising safety concerns.