Convinced for the first time that they can bring down Senate Majority Leader Harry Reid’s (D-Nev.) health care reform package, Republicans are trying to get votes on more amendments as part of a strategy to divide the Democratic Conference and turn a few wayward moderates against the bill.

A group of moderate Democrats have repeatedly joined the Republicans in supporting losing amendments aimed at removing Medicare cuts and tax increases from Reid’s bill, and the GOP believes there are only so many of these losses centrist Members of the majority can stomach before they walk away from the health care package in its entirety.

“We’re being successful at helping the American people understand what this bill costs, what it will do to them, and as a result of that, the American people are turning against the bill and the Democratic Senators are hearing from them,— Senate Republican Conference Chairman Lamar Alexander (Tenn.) said Monday. “They’ve had a steady stream of bad news. I mean, their theme song ought to be, ‘Raindrops Keep Falling on My Head.’—

Senate Minority Leader Mitch McConnell (R-Ky.), unable to reach agreement with Reid on a schedule for voting on additional amendments, moved Sunday to force moderate Democrats to take at least one more tough health care vote by filing cloture on a motion offered by Sen. Mike Crapo (R-Idaho).

Crapo’s motion proposes that families earning up to $250,000 a year — or individuals earning up to $200,000 — do not have their taxes raised to pay for health care reform.

McConnell even said he would give up his usual demand that Republicans get to offer the same number of amendments, as he sought to get an agreement to offer Crapo’s motion in advance of any effort by the Democrats to end debate on Reid’s bill.

Given increased Democratic infighting over the public insurance option, abortion and an amendment by Sen. Byron Dorgan (D-N.D.) relating to the reimportation of prescription drugs, Republicans now believe they have a realistic chance of defeating the majority’s health care package.

“I think the vote tally is going the opposite direction,— Sen. Richard Burr (R-N.C.) said. “You’ve statements out there by [Democratic] Members — what they would support, what they wouldn’t support — that limits very greatly as to where Harry can go to try construct a bill without squeezing the balloon here and having another one pop out.—

A positive Congressional Budget Office cost estimate could turn things in Reid’s favor. But as it stands, the majority conference is divided over a potential compromise to the public insurance option negotiated by a group of 10 liberal and moderate Democrats. Several centrist Democrats expressed concerns over the weekend about Reid’s package and reserved the right to oppose it over key issues.

In particular, Sen. Joe Lieberman (ID-Conn.), already prepared to filibuster over the public insurance option, said he also would vote against a motion to end debate on the bill if it includes a proposal to allow individuals ages 55 to 64 to buy into Medicare.

Sen. Ben Nelson (D-Neb.) is also not keen on the proposal, saying he is prepared to filibuster unless strong language prohibiting federal funding of abortions is added to the bill. Nelson was part of the group of 10 negotiating the public option compromise. Lieberman declined to participate.

Republicans hope to get floor time for additional amendments to target moderate Democrats, including Sen. Jim Webb (Va.), in an effort to at least stop Reid from passing the bill by Christmas, if not kill it altogether.

“At the end of the day, Democratic leaders will be asking their Members to forget about everything they had problems with and voted against, and vote for a [final] product because the president asked them to,— a senior Republican Senate aide said Monday. “It’s an extremely difficult sell.—

Republicans chalk up their success thus far to unprecedented unity — including from moderate GOP Sens. Susan Collins and Olympia Snowe of Maine, who have a long history of joining the Democrats on big-ticket legislation appealing to their liberal-leaning state.

Republican sources say their entire 40-seat Conference agreed months ago to a public relations and legislative strategy, allowing the GOP to be nimble and react quickly to developments. There has been a high degree of cooperation among Senators to push the GOP message to the media, where usually there is much internal bureaucratic haggling.

A group of Republican Senators meet privately every morning to plot that day’s health care strategy. All Members are invited to the meeting, which always features the GOP leadership team and has been heavily attended by Republican Sens. Bob Corker (Tenn.), Judd Gregg (N.H.), John McCain (Ariz.) and Crapo.

One Republican operative off the Hill said the minority is unanimously committed to opposing health care reform as long as Democratic holdouts exist. Snowe, who is the most likely Republican to join the Democrats on health care given her ongoing talks with Reid and support for a public insurance option with a “trigger,— has said privately that she would not be the 60th vote to end a filibuster.

“Republicans realize that the rest of the calendar is starting to work against Reid,— said the GOP operative, who maintains relationships in the Senate. “The GOP strategy is quite simple — do nothing and let every [Democratic] Senator become the decisive 60th vote.—