WASHINGTON — House Speaker Nancy Pelosi on Sunday pledged swift work by Congress on a jobs and infrastructure package that she said would be “fiscally sound” but acknowledged she wasn’t sure whether the next major item on President Biden’s agenda would attract Republican backing.

Fresh off a major legislative victory on the $1.9-trillion virus relief package that passed along near-party lines, Democrats face long and tough battles ahead in winning GOP endorsement of the administration’s plans.

Road- and bridge-building legislation has a long history of support from both parties as lawmakers aim to deliver on projects back home. But Republicans disagree with Biden’s focus on the environment and the possibility of financing any program with debt after the government has borrowed heavily to address the economic fallout from the COVID-19 pandemic.

“Building roads and bridges and water supply systems and the rest has always been bipartisan, always been bipartisan, except when they oppose it with a Democratic president, as they did under President Obama, and we had to shrink the package,” said Pelosi (D-San Francisco).

“But, nonetheless, hopefully, we will have bipartisanship,” she said.

Pelosi has directed key Democratic lawmakers to begin working with Republicans on a “big, bold and transformational infrastructure package.”

During the presidential campaign, Biden laid the groundwork by proposing $2 trillion in “accelerated” investments to shift to cleaner energy, build half a million charging stations for electric vehicles, support public transit and repair roads and bridges. The plan emphasizes the importance of creating unionized jobs and addressing climate change.

The White House originally planned to come out with a plan in February but more recently hasn’t committed to a timeline. A rollout is likely to slide into April as the administration embarks on a nationwide push over the coming weeks to sell Americans on the benefits of the COVID-19 relief bill.

Sen. Thomas R. Carper (D-Del.), chairman of the Senate Environment and Public Works Committee, and Rep. Peter A. DeFazio (D-Ore.), chairman of the House Transportation and Infrastructure Committee, hope to pass a bill out of their committees in May.

The package could include policy changes — on green energy and immigration — and even try to make permanent some of the just-passed COVID-19 assistance such as child tax credits.

“It is going to be green and it is going to be big,” DeFazio said.

Democrats used a fast-track budget process known as reconciliation to approve Biden’s COVID-19 relief plan without Republican support, a strategy that succeeded despite the reservations of some moderates.

But work on passing infrastructure legislation in a Senate split 50-50 with Vice President Kamala Harris providing a tiebreaking vote will probably prove more difficult. Moderate Sen. Joe Manchin III (D-W.Va.) recently made clear he would block infrastructure legislation if Republicans weren’t included.

Wyoming Sen. John Barrasso, the No. 3 Senate Republican, said he wanted to see bipartisan support for an infrastructure legislation. But he said the House in the last Congress modified a Senate-passed $287-billion bill in a way that Republicans could not accept.

“We got it to the House, and what did the House do? They replaced our highway bill with the Green New Deal,” Barrasso said. “So they ignored what we have done in a bipartisan way. If they would take the model that we came up with in the committee in the Senate for highway and transportation, I think that’s a very good start.”

On Sunday, Pelosi declined to say whether tax increases would be required for the House legislation, stressing that Congress would explore all options, including generating revenue with something similar to the Obama administration’s Build America bonds.

“This is about broadband. It’s about water systems. It’s about mass transit. It’s about good-paying jobs all over the country,” she said. “It’s also about schools and housing and the rest.... So the goal is to promote good growth, creating good-paying jobs as we protect our planet and are fiscally sound.”

Pelosi and Barrasso spoke on ABC’s “This Week.”