Progressive Democrats in the House are privately discussing how they can push President Biden for a second spending package substantially bigger than the $3 trillion over a decade floated in various news outlets this week.

Why it matters: These members are attuned to the climate group Sunrise Movement's argument that "the crises we face demand at least $1 trillion per yearover the next decade," two sources familiar with the conversation told Axios.

• Sunrise's extremely ambitious proposal — at least $10 trillion — could quickly emerge as a benchmark for House progressives to rally around.
• "Progressives feel like this package will define Biden's presidency," one source said, "and that $3 trillion over 10 years feels low, and it may not meet the scope of what we need to do — in particular on climate."

The strategy was discussed during a phone call Tuesday among members of the Congressional Progressive Caucus. Several raised concerns about the size of Biden's next spending package, which the president plans to unveil Wednesday in Pittsburgh.

• They regard the reported scope of the proposal — which some moderates such as Sen. Joe Manchin (D-W.Va.) already consider at the far reaches of acceptability — as too small to meet the moment, the source said.
• "He should be bold with his opening offer."

Between the lines: Biden's next spending bill will involve a longer, messier and more complicated fight between the ideological factions of the Democratic Party.

• In the $1.9 trillion COVID-19 relief package that just passed, there was agreement among Democrats from the beginning it was going to be entirely deficit-financed.
• But the next package will likely be more of a running battle. Biden has said he wants to hike corporate and high-income earners' taxes to pay for much of the new spending — which sets up a fight between progressives and moderates.
• And the ambitions for the proposal keep expanding — everything from meat and potatoes infrastructure (roads, bridges, ports), to broadband and climate initiatives.
• There are also proposals for substantial investment in social welfare, including expansion of the child tax credit, universal pre-kindergarten, free community college and other measures.

Bottom line: "The parameters of the battle will not be locked in at the beginning," said the source familiar with the House progressives' internal discussions.

• Progressives will view Biden's announcement next week as an opening framing, "and then Congress is going to have a lot more agency in this fight because it's going to be longer. Congress won't have to act by a certain date."