WASHINGTON (AP) — Democratic moderates who control the balance of power on health care legislation balked Tuesday at a government-run insurance option for millions of Americans, underscoring the enormity of the challenge confronting Senate Majority Leader Harry Reid one day after he unveiled the plan as a consensus product.

Republican opposition stiffened, and party leaders announced they would attempt to strangle the bill before formal debate begins.

Despite the obvious obstacles, senior Democrats cast Reid’s draft legislation as a turning point in the yearlong campaign to enact President Obama’s top domestic priority. Sen. Max Baucus, D-Mont., chairman of the Senate Finance Committee, said there is now a ‘‘sense of inevitability, the sense that, yes, we’re going to pass health care reform, and it’s going to lower costs, provide better health insurance coverage and cover … and reform the health insurance market.’’

The proposed government insurance option long ago emerged as the biggest flashpoint in both the House and Senate as Democrats struggle to pass legislation that extends coverage to millions who lack it, bans insurance industry practices such as denying coverage on the basis of pre-existing medical conditions and slows the growth of health care spending nationally.

But before that issue can be joined on the Senate floor, Reid’s first challenge is to gain 60 votes — the number needed to overcome a filibuster by Republicans — just to bring the bill up, a parliamentary maneuver so routine that a vote is rarely required.

Sen. Mitch McConnell of Kentucky, the Republican leader, announced that in this case, members of his party will treat it as though it were ‘‘a vote on the merits’’ of a bill he said would ‘‘cut Medicare, raise taxes and increase health insurance premiums.’’ He suggested Democrats could expect campaign commercials next year on the basis of the vote, and recalled that Sen. John Kerry, D-Mass., was ridiculed in his 2004 presidential campaign for having once said he voted for a bill before he voted against it.

Tuesday’s developments illustrated the difficulties facing the 69-year-old Reid, juggling at least three separate concerns: his role as head of the Democratic caucus, the desire to deliver on Obama’s agenda and a 2010 re-election campaign in Nevada, where his approval ratings are low.

‘‘This isn’t over until I’m standing with President Obama and he’s signing a bill into law that delivers what Nevadans are demanding — real health insurance reform,’’ Reid wrote in an e-mail message to political supporters in his home state Monday night.

The decision to include a government insurance option in his legislation had obvious appeal for liberals who account for a strong majority inside the Senate Democratic caucus, and it is likely to please labor unions and party activists in Nevada.

But it has gained less-than-effusive support from Obama, who is eager to have at least a dollop of bipartisanship for his signature domestic issue. Sen. Olympia Snowe of Maine, the only Republican who has sided with Democrats in committee this year, has announced she will not support the bill Reid drafted.

Still, if Reid is pressed in coming weeks by moderates to fall back, he can explain to liberals that he was forced to do so because his preference — a government insurance option — proved to be unobtainable in the Senate.

Already, that pressure is evident.

Sen. Tom Carper, D-Del., said he may seek changes on the Senate floor, a move likely to be welcomed by moderates. He backs a government role in states where one or two insurers control the market and premiums are high, along the same lines as a plan supported by Snowe. Additionally, Carper has talked of allowing other states to invite the federal government in — the reverse of Reid’s plan, in which states would have to opt out.

That general approach, in which a lack of competition in an individual’s state would trigger a government insurance option, ‘‘is still alive,’’ said Sen. Kent Conrad, D-N.D.

While Reid is expected eventually to secure all 60 Democratic votes on the critical first test to bring the bill to the Senate floor, Sens. Ben Nelson of Nebraska, Mary Landrieu of Louisiana, Evan Bayh of Indiana and Blanche Lincoln of Arkansas all declined to say on Tuesday how they would vote.

In an indication of the pressure Reid faces, Bayh said the majority leader had agreed to cut an earlier proposal for a $40 billion tax on medical device makers.

‘‘He significantly modified that proposal in a way that I understand will not impact thousands of good-paying jobs,’’ said Bayh, whose state is home to Guidant Corp., a maker of cardiovascular devices, among other major industry players. Numerous officials said Reid had agreed to reduce the new tax to $20 billion over a decade. The officials spoke on condition of anonymity because no announcement had been made.

Speaker Nancy Pelosi is in a similar position in the House. Efforts to draft a consensus health care bill for a vote have been stalled for more than two weeks. The principal stumbling block is an internal disagreement over terms for setting fees for doctors, hospitals and other health care providers treating patients with government-sold coverage.

Liberals want the government to set the rate unilaterally, pegged to the charges the government pays Medicare beneficiaries. Moderates want the government to negotiate with the providers in setting fees.

Pelosi favors the approach liberals want, but officials say she has all but concluded she cannot gain the necessary majority of 218 votes for it.

House Democrats also must resolve internal disagreements relating to abortion services and health care for immigrants before they can send the bill to the House floor for a vote.

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Associated Press writers Julie Hirschfeld Davis, Ben Evans, Andrew Miga, Ken Thomas, Erica Werner and Ricardo Alonso-Zaldivar contributed to this report.