The US Congress starts its new two-year session on Thursday.
"I'm not happy anyone wants to vote against the rules package", McGovern said, but he expressed confidence it would pass.
The request for a decade of tax returns is an increase from initial reports that Democrats would only seek three years.
"The austerians were wrong about the Great Recession and Great Depression", he added. "It is bad economics", Khanna tweeted. "So, she knows what she's doing and that should make you sleep at night - knowing that at least somebody in this town knows what they're doing".More news: Trump wants India, Russia, Pakistan to fight Taliban in Afghanistan
House leaders have announced a package of new chamber rules they plan to pass once the new Congress is sworn on Thursday that Democrats say are created to boost transparency, promote input from rank-and-file members and help defuse perennial standoffs over issues like the debt ceiling.
Michael Zetts, the communications director for Ryan, told Newsweek the congressman had not yet decided how he'd vote on the rules package, but that he did oppose the PAYGO proposition.
Although Pelosi said in a statement afterward that "we welcome the presence of these activists", the episode highlighted a growing rift between establishment Democrats and up-and-coming politicians such as Ocasio-Cortez and Khanna, who each unseated longtime party incumbents. "Critical investments in education, infrastructure, and health care should not be held hostage to budgetary constraints that Republicans have never respected anyhow". Sixteen current and incoming House Democrats signed a letter in November saying they believed, "more strongly than ever that the time has come for new leadership".
Beyond Khanna and Ocasio-Cortez, however, opposition to the proposal appeared muted Wednesday.More news: Billy Donovan is among the candidates UCLA wants for coaching vacancy
However, he changed his mind after Pelosi agreed to a deal about setting term limits for serving as speaker.
The "pay as you go" rule, commonly known as PAYGO, requires that any increase in entitlement spending be offset by cuts in other entitlement programs, or by new revenue raisers, in order to prevent the deficit from increasing.
Several provisions could also make it easier for House Democrats to pass legislation rolling back all or part of the GOP tax cuts, which Democrats have pledged to revisit once they officially assume the majority in the House.More news: Gritty Pujara century puts India in control of Sydney Test