Washington (CNN) Just hours after House Republicans managed to pass a bill to repeal and replace Obamacare, the Senate is signaling it will write its own proposal -- announcing a group of 13 Republican members who will be responsible for crafting the Senate's plan.

All are male.

Senators in the group include Finance Committee Chairman Orrin Hatch, Health and Education Committee Chairman Lamar Alexander and conservatives Ted Cruz and Mike Lee.

A GOP aide defended the makeup of the group.

"We have no interest in playing the games of identity politics, that's not what this is about; it's about getting a job done," the aide said. "We'll work with any member of any background who wants to pass a health reform bill that will reduce premiums and take away the burdens that Obamacare inflicted.

"To reduce this to gender, race or geography misses the more important point of the diverse segments of the conference the group represents on policy -- from members who support Medicaid expansion, to those opposed to it, to those who have called for long term full repeal," the aide added.

The announcement of the health care working group is yet another signal that the bill passed out of the House is merely a starting point for Senate Republicans, who have been saying for months that they had serious concerns about the House's efforts to repeal Obamacare ranging from how the House bill dealt with Medicaid to how it handled people with pre-existing conditions.

Even as the legislation was passing on the House floor, Senate Republicans were admonishing the House's efforts.

"A bill -- finalized yesterday, has not been scored, amendments not allowed, and 3 hours final debate -- should be viewed with caution," tweeted South Carolina Sen. Lindsey Graham

Here are the group of 13 Republicans who will work to build the Senate's bill:

Members of Senate leadership

Majority Leader Mitch McConnell of Kentucky

Sen. John Cornyn of Texas

Sen. John Thune of South Dakota

Sen. John Barrasso of Wyoming

Committee chairmen

HELP Chairman Lamar Alexander of Tennessee

Budget Chairman Mike Enzi of Wyoming

Finance Chairman Orrin Hatch of Utah

Conservatives

Sen. Ted Cruz of Texas

Sen. Mike Lee of Utah

Sen. Tom Cotton of Arkansas

Moderate-leaning

Sen. Cory Gardner of Colorado

Sen. Rob Portman of Ohio

Sen. Pat Toomey of Pennsylvania

This story has been updated.