On Wednesday, Roberts sent Ritter a letter of complaint, which was signed by nine other GOP lawmakers, many of whom are considered moderates in their party.
Ritter angered Republicans last Friday when he signed an executive order allowing the state government to formally bargain with employee unions. Before last week, employees could join a union, but the state did not formally recognize them.
Roberts' letter complained that Ritter made the change without running a bill through the Legislature.
"We disagree with the policy change, but more importantly, we disagree with the way you handled this manner," Roberts wrote.
Ritter's action jeopardizes bipartisan support for big issues like health care, transportation and education, she wrote.
"Those of us who were working with you from the center feel badly betrayed," she wrote.
Evan Dreyer, spokesman for Ritter, said Republicans will get a chance to debate the topic, because they are introducing a bill to repeal Ritter's order.
But he accused Republicans of being demagogues for reacting so furiously to Ritter's "very moderate approach" to unions.
"This is an issue of the CEO of state government creating a framework and establishing some guidelines for how he wants his agency heads to interact with executive branch employees," Dreyer said.
Speaker of the House Andrew Romanoff, D-Denver, said Tuesday he has no problem with Ritter's use of an executive order.
"I think the governor's within his power in this instance," Romanoff said.
Ritter's order forbids strikes or strike threats. It doesn't change the Legislature's power to set state employees' salaries.