The Senate Republican working group on healthcare convened in the Capitol Tuesday with two new senators, including the first woman member to sit in on the discussion.

Sens. Shelley Moore Capito, of West Virginia, and Ron Johnson, of Wisconsin, joined what has grown from a half-dozen to 13 lawmakers who are meeting to determine the fate of the U.S. health insurance system.

Johnson told reporters after leaving the meeting that he is joining the group permanently. It's not clear if Capito will be a permanent member of the group, which focused Tuesday on how to deal with Obamacare's vast Medicaid expansion.

Capito came to the meeting "for a while," according to working group member and Senate Finance Committee Chairman Orrin Hatch, R-Utah. Hatch denied that the group, which as of today had no official women seated on it, is shutting out the opposite sex.

"They are not excluded," Hatch said, when asked about the all-male membership. "They can come anytime they want as far as I'm concerned. I have no problem with that. I like the idea."

Lawmakers left the meeting without any consensus on how to deal with the Medicaid expansion, which was broadened under the healthcare law to include adults earning near the poverty line.

While some Republicans are eager to eliminate the expansion of Medicaid to prevent growing dependency on the federal government, others want to preserve it or phase it out slowly.

"We are going to have to face the music and do what has to be done," Hatch told reporters who asked about the Medicaid discussions. "Once you've got them on the dole they are going to take every dime they can. We've got to find some way to get things under control or this country's future and your future are going to be gone."

Johnson praised the House proposal to phase out the expansion by grandfathering in those who are already signed up. Expansion would eventually end through attrition.

"That's not a bad thing," Johnson said.

Members of the working group said they are waiting for a price-tag for the House-passed bill, which was only partially scored by the Congressional Budget Office. Republicans said that delay is slowing down progress on writing a Senate proposal.

"It does hinder it, so we have to wait," said Senate Budget Committee Chairman Mike Enzi, R-Wyo.

Today's meeting was the first since for the Senate group since the House passed its version of a bill to partially repeal and replace Obamacare.

"The Senate plans to write its own bill, incorporating elements of the House measure.

"We are starting with the House bill and will work from there," Cornyn said. "We are just in the early stages."