"If the free exercise of religion clause of the First Amendment means anything, it means that it is not within the power of the federal government to tell anybody what to believe or to punish them for practicing those beliefs," McConnell said.
"And yet that's precisely what the Obama administration is trying to do through the president's health care law," he continued. "We all remember then- [Speaker Nancy Pelosi (D-Calif.)] saying that we'd have to pass the health care bill to find out what was in it. Well, this is one of the things we've found: that it empowers bureaucrats in Washington to decide which tenets religious institutions can and can't adhere to. If they don't get in line, they're penalized."
The amendment comes in response to a rule put forward by the Obama administration that would require insurance companies to provide and pay for contraception services in accordance with the two-year-old health care law pushed through by Democrats.
The rule initially would have required employers, including religiously affiliated hospitals and universities, to provide insurance that covers contraception, but the White House modified it after taking fire from Catholic groups. Now, insurers bear the burden of offering birth control coverage to women working for religious institutions.
Meanwhile, it's not yet clear whether the House will take up a similar measure.
Speaker John Boehner said Thursday before the Senate vote that he would decide how to proceed in the House after the Senate acted. But he stated, "It's important for us to win this issue.
"It's important that we continue to protect the religious beliefs of the American people from their government," the Ohio Republican said. "I believe that standing up for the Constitution, standing up for people's protection under the law and under the Constitution to practice their belief as they like, is an important part of my job. I'm trying to find a way, frankly, to get a bipartisan agreement to solve this problem."
Just before Boehner spoke, Pelosi, now House Minority Leader, told reporters that the amendment is "extreme" and "a blunt and sweeping overreach into women's health."
"Republicans are kicking of women's history month by bringing the Blunt amendment to the floor," the California Democrat said. It is "part of the Republican agenda of disrespecting women's health issues."
After the press conference, Schumer said Democrats hope to finish work on the transportation bill next week. He said no decisions have been made on what the Senate will consider after, but he added that confirmation of judges, postal reform and bipartisan capital formation bills are possibilities.
Schumer said that the capital formation bills, which have been promoted by House Republicans, are important, but he said passing a highway bill would mean more jobs.
"Is it a panacea? No. Is it a good thing to do? Yes. Is it as important as the highway bill in terms of jobs? No," Schumer said.
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