WASHINGTON — The final lap of the historic health-care marathon is expected to begin Tuesday in the Senate, where Democrats are confident that they have the votes to complete revamping the nation’s health-care system.

First, though, the measure has to survive a last-ditch Republican effort to derail it. Their major challenge is expected to involve Social Security policy, and the outcome could depend on the Senate parliamentarian’s ruling.

The next phase of debate will start after PresidentBarack Obamasigns Senate-authored health-care legislation Tuesday that the House of Representatives approved Sunday night. Once Obama acts, the Senate will consider a package of House changes to that measure called “”reconciliation.””

Debate will be limited to 20 hours, and 51 votes will be needed for passage. Democrats control 59 seats in the Senate, but they expect to lose the votes of some of their conservatives.

Sen.Blanche Lincoln, D-Ark., who faces a difficult re-election campaign, said she’d oppose the measure, charging that the House-drafted reconciliation bill “”wasn’t subject to the same transparency and thorough debate that we used in the Senate.”” Sen.Ben Nelson, D-Neb., also announced that he’ll oppose the reconciliation bill.

Republicans began their Senate assault Monday, as Senate GOP leaderMitch McConnellof Kentucky charged that Democrats “”want us to endorse a raft of new sweetheart deals that were struck behind closed doors last week so this thing could limp over the finish line.””

The White House is countering with its own campaign. Obama plans to promote the bill Thursday in Iowa City, Iowa, where he laid out his health-care proposal as a candidate in 2007.

The reconciliation package, which the House approved Sunday night with no Republican support, would make a series of changes to the bill that Obama will sign Tuesday. It provides more government help with insurance premiums for lower- and middle-class families, more prescription-drug benefits for most Medicare beneficiaries and help for states with Medicaid, the state-federal health program for lower-income people.

The legislation also delays a new tax on high-end insurance policies to 2018, and increases the Medicare payroll tax for the wealthy. Single people who earn more than $200,000 annually, and joint filers who make more than $250,000, would see the tax increase 0.9 percentage point in 2013, to 2.35 percent. They’d also pay a 3.8 percent tax on dividends, interest and other unearned income.

Republicans plan a two-pronged effort to stop the Democratic plan, through parliamentary challenges and amendments.

GOP leaders think they have a potent weapon for the fall midterm campaigns as well as the moral high ground in this debate, and they’re echoing the argument made by Sen.Jim DeMint, R-S.C.

“”Unless this trillion-dollar assault on our freedoms is repealed, it will force Americans to purchase Washington-approved health plans or face stiff penalties,”” DeMint said.

The repeal movement was becoming popular quickly among conservatives.

Former New Hampshire Attorney GeneralKelly Ayotte, a Republican Senate candidate, said Monday that if she were elected, “”I’d be the first to back this bill,”” because “”New Hampshire citizens tell me every day that they don’t want a federal takeover of health care.””

Republicans’ best hope for thwarting the Democrats in the Senate probably lies in the parliamentary process. Under the “”Byrd rule,”” named for master tactician Sen.Robert Byrd, D-W.Va., reconciliation measures must relate directly to the federal budget process.

One key Republican test centers on Social Security. The bill would delay a Senate-approved excise tax on high-end insurance policies by five years, until 2018. That delay, Republicans say, would encourage employers to continue offering more elaborate insurance policies in lieu of increasing wages. Since wages up to a certain level are subject to Social Security tax, the change is likely to mean less Social Security revenue.

Reconciliation isn’t supposed to affect Social Security, Republicans contend. If Senate Parliamentarian Alan Frumin agrees, Democrats could need 60 votes to overturn his ruling — a difficult hurdle — and a failure to get those votes would effectively scuttle the reconciliation bill. Staffers from both parties met with Frumin for an hour Monday and reported no decision.

Democrats claimed to be unconcerned.

“”I’m confident the parliamentarian will see the fallacy of the argument,”” said Sen.Jeff Bingaman, D-N.M.

Amending the reconciliation bill is expected to be difficult, but Republicans see political gain from forcing Democrats to go on the record on controversial issues. Republican leaders are discussing amendments that would reduce the size of proposed cuts to Medicare, cut back the Medicare tax increase and scale back the bill’s $938 billion price tag.