(CNN) When President Donald Trump tweeted Tuesday that he could support a $2 trillion infrastructure package to jumpstart the economy, it was welcome news for House Ways and Means Chairman Richard Neal, a Massachusetts Democrat who has been waiting for months to craft such an effort.

Lawmakers may be away from Capitol Hill, but negotiations have already quietly begun on what could become a fourth stimulus package to respond to the novel coronavirus. House Speaker Nancy Pelosi told reporters Monday that she hopes to include more direct payments for individuals , money for state and local governments and infrastructure funding to address broadband and water systems in such a stimulus bill.

Discussions are taking place between Pelosi, top chairmen of key House committees and Treasury Secretary Steven Mnuchin while Congress is out for most of April, with Democratic leaders aiming to hold a vote in the House when members return. Whether congressional Republicans will support the effort is unclear, but Trump's backing of the infrastructure piece could lend it momentum.

Neal warned that when it comes to infrastructure, Senate Majority Leader Mitch McConnell, a Kentucky Republican, has been "less enthusiastic," but said the President's tweet may help win over some reluctant supporters.

"I think we should go big on it," Neal told CNN of the potential phase four package Tuesday. "The speaker and I have been talking about this for weeks."

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