A Senate working group tasked with crafting a version of health care policy that can muster support from at least 50 of the 52 Republican senators has found its mission complicated by who has not been included — women senators.

The Republican conference includes five women, and none were invited to join a core group of 13 senators to take the lead in crafting a health care bill.

Some Republican women have expressed dismay, including Sen. Lisa Murkowski of Alaska. She told reporters Tuesday, "I just wanna make sure we have some women on" the Senate health care group.

And Sen. Susan Collins of Maine said she wouldn't join now even if she was asked.

"I really don't want to. You know, there are so many important issues in health care that to spend all my time talking about this seems like not a productive way to move forward," Collins said.

But Senate Majority Leader Mitch McConnell said that the group is just one of several discussions ongoing and that every Senate Republican will have a say.

"Nobody’s being excluded based on gender," McConnell said, pointing to an hour-long lunch of Senate Republicans on Tuesday where health care was the main topic of discussion. "What you should write - we’re having a discussion about the real issues. Everybody's at the table. Everybody."

But the "working group," McConnell helped to convene consists of a group of 13 members, including himself, met for the second time on Tuesday before the entire Republican conference met for lunch. At this meeting, the members discussed the topic of Medicaid.

After criticism of the group mounted, Sen. Shelley Moore Capito of West Virginia was invited to join Tuesday's meeting to discuss the health insurance program for low-income Americans, an issue that particularly influences her state.

“Those are choices that were made," Capito said about the makeup of the group. "You know, I don’t know. As a woman I’m going to be participating very loudly.”

“Leaders have the right to choose whomever they wish. It doesn’t mean I’m not going to work on health care,” said Sen. Susan Collins of Maine, a former insurance commissioner and critic of limiting access to abortion providers and who has also co-authored a bill to repeal and replace the Affordable Care Act. “I think I can bring some experience to the debate that will be helpful.”

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Democrats have been quick to point out the lack of women in the group. "I would hope that Senator McConnell would be a little more sensitive to the fact he's picked a dozen men on his side, there are certainly some very competent women he could've chosen," Sen. Dick Durbin, D-Ill., told MSNBC Tuesday. "Let me start with Susan Collins, who's been working on revising and repairing our health care system for some time now, Lisa Murkowski, who has some very strong feelings as well. I mean there are many people he could've turned to have a more balanced approach to a much more affordable repair of the system."

Also missing from the roster are some critical moderate voices. Both Sens. Collins and Murkowski have been skeptical of limiting access to abortion providers.

Related: Democrats Criticize Health Care Working Group For Lack of Diversity

The group does include two notable conservatives — Sens. Ted Cruz of Texas and Mike Lee of Utah — who have wanted nothing short of a complete repeal of Obamacare. But even conservatives say they are leery of McConnell’s move to include them so early in the process to lock in their support.

"We're scared of having our presence be misconstrued as acquiescence," an aide to one conservative senator told NBC News.

For his part, Cruz has already somewhat softened his original position, acknowledging that a complete repeal is untenable.

“The test for success is very simple: will premiums go up or go down,” Cruz said. “And we should start where there is common ground, start where we agree and where there are disagreements. We should look at how we come together to come to yes.”

Sen. Orrin Hatch, R-Utah, noted the impossibility of a full repeal after benefits have been given for nearly a decade.

"The public wants every dime they can be given, I mean, let’s face it once you get them on the dole they’re going to take every dime they can," Hatch said. "And we’ve got to find some way of getting things under control, or this country and your future is going to be gone.”

The gap in policy differences between Republican senators is large, and diffusing the differences is going to be difficult.

Even on the meeting Tuesday to discuss Medicaid, the members of the working group have large differences of opinion.

Sen. Rob Portman of Ohio, a state that expanded Medicaid, is concerned with an abrupt end to the expansion that he says has helped Ohio residents. He floated adding increasing the tax credits for low-income people if the Medicaid expansion is cut.

“I'd like to change the House version of the tax credit by the way and focus it more on people who are close to the poverty line rather than having it at the higher end,” Portman told reporters.

On the other end of the ideological spectrum, Sen. Lee wants to end the Medicaid expansion and reduce the number of people receiving it by restricting it to expectant mothers, the disabled and caregivers of young children.

In addition, Lee wants a repeal of all insurance mandates, including essential health benefits and even pre-existing conditions, which is politically explosive. The House bill has been criticized for amendments that would allow people with pre-existing conditions to be charged more.

But Sen. Lamar Alexander, chairman of the Senate Health, Education and Labor Committee, who is on the working group, said that one of his four priorities is to “make sure people with pre-existing conditions have access to health care.”

Senators say they are aware of the policy challenges and are cautioning against any legislation being introduced soon.

“We're going to have to satisfy 51 senators. And I can't tell you how long that's going to take. ... We don't have any arbitrary deadline,” said Sen. John Cornyn, the second highest ranking Republican in the Senate. “But it's going to take some time to get to that consensus.”

Meanwhile, all 48 Democrats, including the two independents who caucus with the Democrats, wrote a letter to McConnell asking him not to gut Obamacare and instead work with them to make health care better.

“Democrats stand ready — as we always have — to develop legislation with Republicans that will improve quality, lower costs, and expand coverage for all Americans. But Republicans need to set aside their current partisan efforts and work with us to get this done,” the Democrats wrote in the letter.

Vice President Mike Pence attended a Senate luncheon Tuesday to discuss health care, among other issues. Pence could be a critical vote in the Senate — if Republicans lose just two of their members, he would be in a position as president of the Senate to break a tie.