Among them: her own running mate, Ajamu Baraka, who told CNN on Tuesday: "I'm not in favor of the recount."
Baraka said he had spoken with Stein about his concerns, telling her "it was a potentially dangerous move" because it could be mischaracterized by the broader political community.
"It would be seen as carrying the water for the Democrats," Baraka said.
The former third-party vice presidential nominee had earlier expressed his thoughts on Facebook, where he vouched for Stein's ethics and intentions while outlining his concerns her effort could undermine the Green Party's independence.
"The recount effort has resulted in serious questions regarding the motivations of the recount that threatens to damage the standing and reputation of the Green Party, its supporters and activists," Baraka wrote on Facebook
Stein has said the recount is about building confidence in the election results themselves, telling CNN's Anderson Cooper it "is a deeply felt need of voters coming out of this deeply painful election."
The Green Party's Maryland Senate candidate Margaret Flowers has circulated an open letter
, which has signatures from many prominent Green Party members, opposing the recount.
"While we support electoral reforms, including how the vote is counted, we do not support the current recount being undertaken by Jill Stein," the letter said.
Flowers told CNN in a separate interview on Tuesday her letter came from internal "cross-talk" between members of the Green Party in the wake of Stein's announcement and concerns the recount gave the Green Party -- a third-party to the left of and in opposition to the Democratic Party -- the appearance of coming to the aid of Hillary Clinton.
Stein has chosen to target Michigan, Pennsylvania and Wisconsin -- three states Clinton narrowly lost to President-elect Donald Trump.
Stein has steadfastly denied she is trying to help Clinton and acknowledged to Cooper Monday that her recount effort was unlikely to change the results of the election.
Flowers also denied that the recount effort was an attempt by Stein to fundraise for her party -- as Trump has alleged -- calling her committed to the cause of "election integrity," a sentiment Baraka echoed verbatim.