WASHINGTON (Reuters) -President Joe Biden made the case for his sweeping, two-track infrastructure initiative on Capitol Hill on Wednesday, a day after leading Senate Democrats agreed on a $3.5 trillion plan billed as the biggest boost in decades for U.S. families.

Biden joined fellow Democrats for a closed-door lunch where he sought their support and discussed strategy for passing both a $1.2 trillion bipartisan infrastructure deal to rebuild America's roads and bridges, and the larger Democratic package that also addresses climate change and the need for stronger social services.

"We're going to get this done," Biden said as he walked into the meeting with Democratic senators.

Republicans voiced immediate objections to the plan's massive size, as did at least one key moderate Democrat whose support would be critical to passage.

Biden urged senators to think about how the package would affect average Americans, said Senator Chris Murphy.

“He just kept on telling us to think about his neighbors in Scranton," Murphy said, referring to Biden's Pennsylvania hometown. "Think about whether what we're doing is going to pass muster with the folks that he grew up with."

An Ipsos poll conducted this month for Reuters found that most Americans want the kind of infrastructure improvements that are included in the Biden plan. It also found that nearly two-thirds of the country supports increasing taxes on "the highest-earning Americans" to pay for the improvements.

Democrats face a tricky path ahead in getting the two measures approved by a narrowly divided Congress. They will need the support of all 50 of their senators - plus Vice President Kamala Harris' tie-breaking vote - to pass the $3.5 trillion over Republican opposition in the 100-seat Senate, using a maneuver called reconciliation that gets around the chamber's normal 60-vote threshold to pass legislation.

Elements of the $3.5 trillion plan also would have to pass muster with the Senate parliamentarian, who has the power to rule specific provisions ineligible for inclusion under the special reconciliation rules for that legislation's consideration.

While some of the more liberal Democrats on Wednesday said they had hoped for a bigger plan, they had yet to reject the $3.5 trillion deal.

"The need is so much greater than what we’re providing. But still, this is very significant," Senator Mazie Hirono told reporters.

As the day wore on, Democrats across Capitol Hill tried to demonstrate unity over the 10-year investment framework. House of Representatives Speaker Nancy Pelosi called it a "victory for the American people."

And just as Biden was leaving the Capitol, he got a boost from the head of the Congressional Progressive Caucus, a nearly 100-member group of lawmakers whose support is essential.

"We are still looking at all the details but we certainly see this as important movement forward," said Democratic Representative Pramila Jayapal, who heads the group.

Democratic Senator Joe Manchin, an outspoken moderate, stressed the need to offset the $3.5 trillion cost amid large budget deficits.

Manchin also fretted that the plan could eliminate subsidies for fossil fuels, a key demand from progressives worried about climate change.

"Anybody moving in a direction where they think they can walk away and not have any fossil in play, that's just wrong. It won't happen," said the senator, who represents the coal-mining state of West Virginia.

Senate Finance Committee Chairman Ron Wyden, whose panel oversees tax legislation, said a Democratic plan to raise international taxes on corporations would raise "several hundred billion dollars" on its own.

REPUBLICANS SAY TOO PRICEY

Senate Republican Leader Mitch McConnell wasted no time in going on the attack.

"With inflation raging ... (the Democrats' budget plan) is wildly, wildly out of proportion to what the country needs right now," he told reporters.

U.S. consumer prices rose by the most in 13 years last month amid supply constraints and a rebound in the costs of travel-related services from pandemic-depressed levels as the economic recovery gathered momentum, according to data released on Tuesday.

Republican Senator Rob Portman dismissed any notion that the level of spending being proposed would sink prospects for passage of the smaller, bipartisan bill. A group he leads plans to provide details on the legislation in coming days.

Even if they pass the Senate, both measures would also need to make it through the House before going to Biden's desk for signing into law.

The $3.5 trillion plan agreed to by senior Democrats and White House negotiators includes a significant expansion of the Medicare healthcare program for the elderly - a top goal of Senate Budget Committee Chairman Bernie Sanders, who joined Democratic Senate Majority Leader Chuck Schumer in unveiling the deal Tuesday night.

Senate Republicans, who assail Biden's larger spending ambitions as unnecessary, have voiced qualified support for the narrower $1.2 trillion plan, which includes nearly $600 billion in new spending for roads, bridges, rail, public transit, water and broadband internet systems.

The Senate's 50 Republicans are not expected to back the broader infrastructure effort, which would undo Republican then-President Donald Trump's 2017 tax cuts by raising taxes on U.S. corporations and wealthy individuals.

Asked about the Democrats' deal on Wednesday, Republican Senator Mitt Romney said in a brief interview in the Capitol, it was “stunning. It’s a shocking figure, particularly at a time when the economy is already heating. It seems that our Democrat friends may have lost their bearings.”

(Reporting by David Morgan, Susan Cornwell, Richard Cowan, Trevor Hunnicutt and Susan Heavey; Editing by Scott Malone, Howard Goller and Jonathan Oatis)