As Washington considers other steps for responding to the coronavirus pandemic and the resulting economic damage, President Donald Trump and House Speaker Nancy Pelosi both have suggested a “Phase 4” package could include spending on infrastructure.

Trump on Tuesday called for $2 trillion in spending on infrastructure, saying in a tweet that it was time to “be VERY BIG & BOLD” while interest rates are low.

The president’s statements on Twitter come after Pelosi on Monday said a “Phase 4” coronavirus stimulus package ought to include a bipartisan deal on infrastructure spending. In his tweets on Tuesday, Trump used the term “Phase 4” and said Pelosi “wasn’t bad” in a TV appearance on Tuesday.

The California Democrat on Monday also said she would like to see the next bill feature “more direct payments” to Americans, more money for state and local governments, increased protections for workers, more assistance for hospitals and nursing homes and “more opportunity for family and medical leave.”

“The president said during the campaign — and since — infrastructure was a priority for him. So that’s why we believe that in terms of recovery, that’s probably the most bipartisan path that we can take,” Pelosi said on Monday in a conference call with reporters.

Trump’s tweets may allay concerns that he isn’t interested in a bipartisan deal on infrastructure. Analysts at Beacon Policy Advisors warned on Monday that while infrastructure is “naturally a policy area of interest” for Trump, there were “no clear infrastructure proponents as of now” who have his ear on this topic.

“Still, infrastructure will be an important policy area to watch over the next few months,” Beacon’s analysts said in a note. “With low borrowing rates and a greater tolerance for deficit spending, some sort of infrastructure legislation could be enticing to include in the continuing response to the coronavirus pandemic.”

Senate Majority Leader Mitch McConnell, for his part, said on Tuesday that he was taking a wait-and-see approach to a possible “Phase 4” package.

“Any kind of bill coming out of the House I would look at like Reagan suggested we look at the Russians – ‘Trust, but verify,’” the Kentucky Republican told talk show host Hugh Hewitt. “So let’s see how things are going, and respond accordingly. But let’s not, I’m not going to allow this to be an opportunity for the Democrats to achieve unrelated policy items that they would not otherwise be able to pass.”

House Minority Leader Kevin McCarthy, the California Republican, has questioned whether a fourth response bill is necessary.

“I’m not sure we need a fourth package,” McCarthy told Fox News on Sunday. “Before we go to start drafting a fourth package, I’d like these three packages we just put out — remember, it’s more than $2 trillion, the largest we’ve ever seen — to take care and get this economy moving.”

But the White House is preparing for a fourth measure and government agencies have requested a total of about $600 billion, according to a Bloomberg News report citing unnamed sources. The requests include more state aid and assistance for mortgage markets and the travel sector.

On Tuesday, Pelosi said on MSNBC that the fourth bill would focus on “the recovery,” after the first two packages were aimed at “the emergency” and the third on “mitigation.” She identified broadband internet as another area of coming focus since “so many people are relying on telecommunication and social media.”

A year ago, Trump and top Democratic lawmakers reached a deal on a $2 trillion infrastructure plan, but the agreement unraveled within weeks. Earlier this year, House Democrats put forth a $760 million infrastructure proposal.

“In terms of working with the GOP, I think the coronavirus pandemic has really kind of bared a lot of the inadequacies, if you will, with the nation’s infrastructure,” said Democratic Rep. Frank Pallone of New Jersey, who chairs the House Energy & Commerce Committee, on Monday. “For example, if you just use the health-care system, we’re now reopening hospitals that were closed.”

Congress is on recess and slated to get back to work on April 20, though lawmakers could return sooner or later than planned. A growing number of legislators have voiced support for remote voting, but operating that way doesn’t look likely in the near term, with a House Rules Committee report pouring cold water on the idea last week.

A fourth stimulus package is unlikely to pass before late May, and lawmakers won’t be remote voting in the foreseeable future, predicted Henrietta Treyz, director of economic policy research at Veda Partners, in a note on Tuesday. She added that Pelosi has floated the idea of rolling back the cap on state and local tax (SALT) deductions, but that’s “political dynamite” and won’t pass though it could lead to fighting and media attention.

A fourth coronavirus bill is likely to involve at least in part “technical corrections” to the $2 trillion stimulus bill that Trump signed into law on Friday. Last week’s legislation is considered Washington’s “Phase 3” response to the coronavirus causing the disease COVID-19. It follows a mid-March bill targeting paid leave and testing, as well as an initial $8.3 billion emergency spending plan that came together in early March.