Fresh off a major legislative victory on the coronavirus relief package, President Biden is facing a new round of battles on the next pieces of his agenda — exposing divisions within the Democratic Party not only on policy merits but also on how they get it accomplished.

On infrastructure — so high in its potential for bipartisanship that it has become a Washington cliche — Senate Democrats are already confronting an internal dispute over whether to use a party-line procedural tool that would allow them to pass a bill with no GOP support. Biden’s comprehensive immigration overhaul — a “Day One” priority for the president — is also struggling to gain traction even in the House, as Democratic leaders begin an uphill battle to count votes in favor of a sweeping bill.

And that’s before Democrats begin grappling with the hurdle that is the Senate filibuster.

The complicated dynamics among Democrats on Capitol Hill show that getting the type of unity the party attained on the virus relief measure will probably be more difficult for Biden and congressional leaders on immigration, infrastructure and other issues.

Corralling near-unanimous support will be key considering few Democratic lawmakers are showing much appetite for negotiating with Republicans, particularly if it means watering down their ambitious priorities ahead of the 2022 midterms. But House Speaker Nancy Pelosi (D-Calif.) and Senate Majority Leader Charles E. Schumer (D-N.Y.) have little room for error, with the Senate split evenly and a House Democratic caucus that, by next week, is set to have only an eight-vote majority over Republicans.

“You’ve got to be ready on both fronts,” said Senate Finance Committee Chairman Ron Wyden (D-Ore.). “I’m going to do everything I possibly can — you’ve seen the president’s remarks — to make this next round bipartisan. But if it becomes clear that there’s just no real interest in that, then you’ve got to be ready to meet the needs of the public.”

The White House so far has not said what Biden will turn to next as part of his legislative agenda. Press secretary Jen Psaki has maintained that the administration is focused on implementing the massive, $1.9 trillion coronavirus relief package that the president signed into law Thursday.

Psaki nonetheless signaled that both immigration and infrastructure are top priorities. On the former, she said Biden’s proposed immigration overhaul would be a potential panacea to the growing crisis on the U.S.-Mexico border, considering its focus on addressing the root causes of migration from Central America and surging additional resources toward the region.

“Given all of the concern by many in Congress about immigration and what’s happening at the border, this sure seems like a good time to move that initiative forward,” Psaki said this week. She declined to outline any components of a potential jobs and infrastructure package.

But behind the scenes, the prospects of Biden’s immigration bill surviving through Congress intact appear increasingly bleak. House Democratic leaders have privately started to gauge the level of support for the president’s plan — formally called the U.S. Citizenship Act — and found that, at this point, it would struggle to pass, according to people familiar with the matter.

Scores of new lawmakers haven’t tackled immigration previously and know little about the issue. Many lawmakers also feel that such a massive overhaul is moving too quickly in the House, while moderates fear supporting controversial legislation that has no real path in the Senate, said the people, who spoke on the condition of anonymity to discuss private Democratic caucus dynamics.

Some moderates had indicated that they would oppose Biden’s immigration legislation if it were fast-tracked to the floor for a vote primarily on process objections rather than on its substantive merits, these people said. White House officials have conducted at least one staff-level briefing for Congress on Biden’s plan, but there has been little administration engagement otherwise so far, according to aides and lawmakers.

“I do think it is the most comprehensive, progressive immigration bill that we have seen in a long time,” said Rep. Pramila Jayapal (D-Wash.). But she acknowledged that Democrats still have work to do among their own ranks, adding, “We’re still getting everybody to know what is in the bill.”

Some House Democrats have privately suggested bolstering immigration enforcement measures in Biden’s plan to increase the chances of attracting Republican support, particularly in the Senate. But any significant expansion of security and enforcement measures could drain backing from liberals who dominate the Democratic caucus.

Rep. Tom Malinowski (D), who represents a swing district in suburban New Jersey, said that while he supports Biden’s immigration plan, he is also advocating for provisions that would require employers to use a worker verification system. The president’s legislation includes a commission to study the system, known as E-Verify, but no mandate for businesses to use it.

“As a moral matter, I think it makes sense to shift the burden of enforcement away from poor families who are trying to make a life for themselves to employers who are responsible for generating the flow of undocumented immigrants to the United States,” Malinowski said.

He added: “I don’t want to just pass a bill in the House. I want to actually change things.”

So while they sort through internal dynamics on the broader overhaul, House Democratic leaders will move smaller, more targeted legislation that would offer a pathway to citizenship for beneficiaries of the Deferred Action for Childhood Arrivals program and immigrants who have been shielded from deportation under temporary protected status. House Democrats will also pass legislation that offers green cards to farmworkers who don’t have legal status.

Those two bills are expected to pass next week. The administration has maintained that they are open to piecemeal revisions of U.S. immigration laws rather than the president’s comprehensive overhaul.

“They’re not wedded to that plan,” one advocate in touch with the White House said of Biden’s immigration proposal. “They’re willing to make any relief for the undocumented.”

Meanwhile, Senate Judiciary Committee Chairman Richard J. Durbin (D-Ill.) said he plans to take up “some parts” of Biden’s immigration proposal through his committee but also said that the legislation would not pass the Senate in its current form.

Instead, Durbin — also his party’s chief vote counter — has quietly spoken to Republican senators, including some he called “unlikely suspects,” to see whether he can build a coalition of bipartisan support for smaller chunks of legislation, such as legalization for immigrants who came to the United States as children.

“I wanted to see what was possible,” Durbin said. “If [the Dream Act] and farm labor are their starting points [in the House], I want those starting points to be on the table here in the Senate.”

As lawmakers begin moving on immigration, Biden — at least through his Oval Office meetings — has telegraphed that infrastructure may be the more immediate priority, convening at least two bipartisan gatherings with House and Senate members.

The White House has declined to say whether Biden would be open to the fast-track parliamentary measure used for coronavirus relief — called reconciliation — on infrastructure, with officials noting that the president hasn’t even proposed a bill.

But two of the most influential forces in the Senate Democratic caucus are colliding on strategy.

Sen. Joe Manchin III (D-W.Va.) is insisting that Democrats avoid using reconciliation on infrastructure, considering its record as a historically bipartisan issue.

But Sen. Bernie Sanders (I-Vt.) — the chairman of the Senate Budget Committee, who is in charge of crafting reconciliation strategies through his panel — signaled that doing so would be the only way of getting a meaningful infrastructure package accomplished.

“I want to get it done,” Sanders said when asked this week why he was pursuing the reconciliation path. “So if 10 Republicans come up to me today and say that, ‘We’re serious about major legislation,’ that would be great. But based on what I’ve seen up to now, I haven’t seen that.”

Ultimately, what Biden himself wants will be key. Unlike coronavirus relief, infrastructure is not pressing up against an urgent deadline.

In meetings with lawmakers on the issue, Biden has largely declined to detail his own priorities, instead preaching the virtues of cross-party cooperation and soliciting ideas from lawmakers, according to attendees. White House advisers including Brian Deese, the director of the National Economic Council, have followed up privately with GOP senators.

“The bipartisanship was certainly something that the president talked about,” said Rep. Sharice Davids (D-Kan.), who met with Biden last week. “It seemed a lot of just, like, ‘Let’s all keep an open mind and figure out where we can find some common ground.’ ”

Sen. Shelley Moore Capito (R-W.Va.), who met with Biden and a handful of senators in a late February meeting, said: “I keep pleading for bipartisanship and, ‘Let’s keep it within the guardrails of what we know we can accomplish.’ ”

On the push from some Senate Democrats to tackle infrastructure without Republican buy-in, Capito said: “It just smacks of totally opposite of what the president said and the signals that we were having.”