Sen. Ted Cruz, Texas Republican, referred to the Affordable Care Act as a "colossal mistake" in rolling out a bill with nine GOP co-sponsors to permanently strip the overhaul of funding.
Opponents of Mr. Obama's law are jumping on the White House's sudden decision to delay, until 2015, an "employer mandate" requiring businesses with more than 50 workers to provide health coverage or pay fines.
Republicans said Mr. Obama had no right to pick and choose which parts of the law go forward, while Democrats accused GOP leaders of obstructing the law at every turn.
Sen. Marco Rubio, Florida Republican, called on colleagues Thursday to oppose any short-term spending bill that funds the health care law. Hours later, Mr. Cruz unveiled his legislation.
"The administration's selective enforcement of Obamacare's implementation is no indication that the law is going away," Mr. Cruz said. "To the contrary, it demonstrates the president's unyielding determination to force the unworkable law on the American people."
Although House Republicans have voted repeatedly to repeal the law, Mr. Cruz's effort will face an uphill battle in the Democrat-controlled Senate.
Sen. Jerry Moran, Kansas Republican, tried — and failed — on Thursday to offer amendments to an appropriations bill that would defund the law's employer mandate and a second mandate that requires individuals to acquire insurance.