Joe Biden’s economic vision has taken a major step toward becoming reality after the US Senate passed two infrastructure measures, but widening political divisions within the Democratic party could yet derail the entire legislative package.

The Senate last week advanced a sprawling $3.5tn budget blueprint for “soft” infrastructure projects to tackle climate change and health care, a day after approving a $1tr bipartisan infrastructure bill to rebuild the nation’s crumbling roads and bridges.

But even as Senate Democrats congratulated themselves on pushing through both measures, the fate of Biden’s economic priorities rests on House Democrats clearing several more looming hurdles as well as uniting the party’s left and right.

The challenges facing the two infrastructure measures reflects the difficulty in trying to force bipartisan compromise in a deeply divided House and Senate where the Democrats possess only narrow majorities.

Liberal Democrats who have bristled at seeing their top climate and social priorities jettisoned as Biden sought an elusive bipartisan compromise with moderate Senate Republicans may seek to change elements of the package, which could upend the delicate legislation.

At a minimum, progressives have insisted the House delay considering the bipartisan infrastructure bill until the Senate passes a far larger climate and health bill – something not expected until the fall, and against the hopes of centrist House Democrats.

In order to deliver the president’s agenda, Democrats are pursuing a two-track approach that involves Congress passing both measures, starting with the $1tn bipartisan compromise that funnels $550bn of new money into traditional infrastructure projects.

The second half of the strategy involves the House and Senate passing the climate and health bill, crafted on the basis of the $3.5tn budget blueprint, and passed using reconciliation, a fast-track process that allows Democrats to bypass a Republican filibuster – a procedural convention that can derail legislation.

The Democrats’ plan is backstopped by an ironclad commitment from the speaker, Nancy Pelosi, that the House will not take up the bipartisan infrastructure bill until the Senate first passes the reconciliation bill, which will take weeks to hammer out in the 50-50 Senate.

The move by Pelosi is aimed at trying to balance the competing demands between progressives demanding maximum spending and more fiscally conservative centrists – all while ensuring that both measures are in the end enacted.

When the speaker navigated through a similar two-track strategy to approve the Affordable Care Act under President Barack Obama in 2010, the bill passed notwithstanding the defections of three Democrats in the Senate and three dozen in the House.

Pelosi now holds such a razor-thin majority in the House that she can afford only three Democratic defections to pass the bipartisan bill and the reconciliation bill if the votes are along party lines. Protest votes from either faction could sink the entire effort.

But growing discontent about the legislation on both sides on Capitol Hill signals the prospect of an even more bitter and protracted intra-party fight over the future of the legislation in the coming weeks and months.

The speaker on Wednesday reaffirmed her position to House Democrats during a closed-door caucus meeting that the Senate would have to first pass the $3.5tr reconciliation bill before the House would move to consider the bipartisan bill.

“The votes in the House and Senate depend on us having both bills,” Pelosi told House Democrats, referencing the thin majorities in both chambers, according to a source familiar with the speaker’s remarks.

That means the Senate majority leader, Chuck Schumer, will need his committee chairs to finalize the language for the reconciliation bill and gain the approval of centrist Senate Democrats Kyrsten Sinema and Joe Manchin before the House can proceed.

In an added complication, both Sinema and Manchin have sounded the alarm in recent days over the cost of the $3.5tr budget blueprint that will guide the reconciliation bill, though they joined their colleagues in voting to allow the framework to pass.

The possibility that Democrats could get both the bipartisan infrastructure bill and the reconciliation bill has outraged Republicans, who have vowed to try to derail the $3.5tr package, which Senate GOP leader Mitch McConnell likened to a “reckless tax-and-spending spree”.

Challenges in the House also returned on Friday after a group of nine House Democratic moderates threatened in a letter to vote against the $3.5tn budget blueprint when the House returns the week of 23 August, if Pelosi didn’t pass the bipartisan bill first.

The missive called on the speaker to abandon her two-track timetable so members vulnerable in 2022 could sell the bill to voters. “We will not consider voting for a budget resolution until the bipartisan Infrastructure Investment and Jobs Act passes the House and is signed into law,” the nine moderates wrote in a letter, which a House Democratic leadership aide described as “highly problematic”.

Threats from moderates have infuriated progressive Democrats, who, emboldened by their successful effort to twist the Biden administration to introduce a new eviction moratorium, have repeatedly warned House Democratic leaders not to deviate from their original plan.

In a letter to Pelosi on Tuesday, the leaders of the Congressional Progressive Caucus said a poll of their 96 members confirmed a majority would withhold their support for the bipartisan infrastructure bill until the Senate passed the reconciliation bill.

White House officials have said that they remain closely attuned to the growing tensions in the House and Senate. Pelosi and Biden speak regularly, and aides have started holding thrice-weekly conference calls, according to sources familiar with the matter.

But top Democrats in Congress see no alternative to the path they are headed down and are hopeful that the two-track strategy will prove successful as in 2010. “I am very pleased to report that the two-track strategy is right on track,” Schumer said.