Washington (CNN) -- Senate Republicans on Wednesday launched an attempt to amend or kill legislation expanding the recently enacted health care reform law -- part of a GOP pledge to use every parliamentary tool available to undermine the measure.

The amendments also are designed to force Democrats to cast unpopular votes in the run-up to this November's midterm elections.

Senate Democrats easily defeated the first of the amendments, which challenged provisions in the bill involving changes to Medicare funding.

Also defeated were attempts to send the measure to committee for reconsideration -- which would effectively kill it -- and other amendments intended to strip provisions from the bill. There were at least 11 other motions or amendments to be considered.

The Democrats' so-called fixes bill was necessary to get a reluctant House of Representatives to pass the Senate's health care reform measure Sunday night.

The House's narrow approval of the measure allowed President Obama to sign it into law Tuesday, giving the president a victory on his signature domestic issue. But in return, House Democrats are now expecting the Senate to sign off on the compromises included in the fixes bill.

The compromise package would add more than $60 billion to the overall plan's cost partly by expanding insurance subsidies for middle- and lower-income families. It would also expand Medicare's prescription drug benefit while scaling back the bill's taxes on expensive insurance plans.

While Obama is pushing to get the measure to his desk, Democrats have acknowledged they are concerned that the Republicans may succeed in changing the carefully balanced package.

Any changes would force the package back to the House for another vote.

Also Wednesday, Democratic senators complained that Republicans had shut down committee hearings for a second straight day as part of a strategy of obstruction in protest of the health care bill.

Sen. Carl Levin, D-Michigan, and Sen. Claire McCaskill, D-Missouri, told a news conference the GOP tactic was delaying work on vital issues.

"It's unconscionable," said Levin, who as chairman of the Armed Services Committee was supposed to conduct a hearing with a top U.S. military commander in Korea who had flown in for the hearing. "Out national security cannot be held hostage to disagreements over a health care policy."

McCaskill had planned an oversight hearing on problems with contracts to train local police departments in Afghanistan. She said the Senate rule that allows the minority party to block committee action was "really dumb" and should be dropped.

"Disagree with us, debate us, vote no," she said. "But to use a rule to stop us from working -- that dog just doesn't hunt from where I come from. That doesn't even makes sense. That's why people in American think we are clueless here."

Levin said he "pleaded" with Senate Minority Leader Mitch McConnell of Kentucky to prevent the blocking of a second day of hearings. A GOP objection Tuesday also closed down committee work.

"It seems to me this is an example of how the obstructionism around here has gotten mindless," Levin said.

A GOP leadership aide would not directly respond to Levin's charge but noted that Democrats canceled hearings Tuesday so that senators could attend the White House signing ceremony for the health care bill.

Among the amendments being proposed by Republicans is a provision to prevent the bill's planned Medicare cuts from being used to finance other programs. They also are proposing to eliminate new penalties being imposed on businesses whose workers use federally subsidized insurance.

Sen. Tom Coburn, R-Oklahoma, has proposed that drugs for erectile dysfunction, such as Viagra and Cialis, be prohibited to sex offenders.

iReport: How will health care reform affect you?

Sen. John McCain, R-Arizona, is pushing to strike so-called "sweetheart deals" such as an extra $300 million in Medicaid funds for the state of Louisiana. Critics have labeled the deal the "Louisiana Purchase."

Democrats have dismissed the GOP proposals as little more than politically motivated obstructionism meant to derail the deal.

Republicans are "not serious about helping this bill," Senate Majority Leader Harry Reid, D-Nevada, said Wednesday. They are concerned only with "throwing roadblocks in front of anything we do."

Reid said Senate Democrats "feel very comfortable and confident" that the package of changes as currently drafted will pass.

House Majority Leader Steny Hoyer, D-Maryland, said Tuesday he didn't think the Senate would change the bill, but if it did, the House would be prepared to vote on the revised bill and send it to Obama.

After a White House meeting Monday night with Senate Democratic leaders and Obama, a senior Democratic source said they believe some portions of the fixes bill may be ruled out of order because they violate the complicated legislative rules governing the process. The source would not specify the potential problems identified at the meeting.

Senate Finance Chairman Max Baucus, D-Montana, said one or two potential problems were identified, but he said they were minor.

Watch senators talk about opposition to reform

Once Republicans raise a point of order, it would be up to the Senate parliamentarian to rule on whether it is legitimate. Democrats would have difficulty defeating a point of order because that would require 60 votes. The Democrats lost their filibuster-proof 60-seat majority in the chamber when Republican Scott Brown won the Massachusetts seat long held by Democrat Ted Kennedy, who died last year.

The loss of the 60-seat supermajority was what prompted the complicated two-bill strategy being used by the Democrats. If the House had made any changes to the Senate version of the bill, it would have had to go back to the Senate for another vote. It would have stalled there, because Republicans have enough seats to filibuster it.

Democrats therefore approved the Senate bill without changes and proposed the fixes bill, which they are trying pass in the Senate through reconciliation, which allows bills affecting the budget to pass by a simple majority of 51 votes.

The points of order that Republicans are expected to raise would deal with aspects of the legislation that they say violate the strict rules on the reconciliation process.

In an ironic twist, many of the provisions of the fixes bill that Republicans are trying to kill were backed by Republicans during debate on the Senate health care bill. For example, the fixes bill would eliminate a provision for the federal government to pay Medicaid cost increases for the state of Nebraska, a provision that was negotiated by Democratic Nebraska Sen. Ben Nelson in exchange for his support.

Republicans cited the Nelson trade-off as an example of what they called unethical deal-making by Democrats to get the health care bill passed in December.

CNN's Tom Cohen, Alan Silverleib Ted Barrett and Deirdre Walsh contributed to this report.