WASHINGTON (Reuters) - Barely two days into crafting a new bill to roll back Obamacare, U.S. Senate Republicans were already on the defensive on Tuesday over the absence of any women in their core working group. After a meeting of the Senate healthcare group, lawmakers were bombarded with questions as to why no women were named to the 13-man panel. Senate Majority Leader Mitch McConnell tried to explain. “The working group that counts is all 52 of us,” McConnell told reporters, referring to all 52 Republican senators in the 100-member chamber. “Nobody is being excluded based upon gender ... Everybody’s at the table. Everybody.” Democrats pounced. Republican men are negotiating “a secret healthcare plan, which I really hope is not happening in the men’s locker room,” said Senator Patty Murray, a member of the Democratic leadership from Washington state.      If the criticism was any sign of what lies ahead as senators try to improve on a rollback bill passed on Thursday by House of Representatives Republicans, it could be a long road ahead. Dismantling the parts of President Barack Obama’s signature healthcare law that they dislike and preserving other parts of it is proving to be a difficult task for President Donald Trump and his fellow Republicans. A House of Representatives’ plan for doing that, approved last week amid much drama, faces an uncertain future in the Senate. Some Republicans eye drafting a similar Senate bill by mid-summer, possibly with the involvement of Democrats. Others indicate the House bill requires major surgery and that the effort to replace the Affordable Care Act, also known as Obamacare, could take months.  Regardless of timing, two decisive factors will come into sharper focus soon. One is voter reaction to the House bill, now being voiced in town hall events being hosted nationwide by House members in their home districts. The other factor is an expected analysis by the non-partisan Congressional Budget Office of how many million Americans would lose their health insurance coverage under the House bill, if it became law, and how it would affect the U.S. budget deficit. Both the CBO analysis and the town hall events have the potential to do damage to the House legislation, which Trump hailed as a triumph just days ago. Senators are already talking about major changes in the House bill concerning Medicaid, the government healthcare program for the poor, and tax subsidies for healthcare coverage. Trying to get past the controversy over the absence of women on the healthcare panel, Senate Republicans said they expected to devote much time to healthcare in the near future.  “I don’t think we’re going to be talking about much else other than healthcare at least three days a week with all members of our conference present,” said Senator John Cornyn, the No. 2 Republican. Cornyn said senators would start with the House bill. “If we have to make modifications in order to pass it, we’ll make those modifications and work out the differences with the House.” Medicaid was the topic at the Senate working group meeting  Tuesday. The House bill would cut federal spending on Medicaid by $880 billion over 10 years. But some Republicans want any reductions to be more gradual, and Trump made a campaign pledge not to cut the program. “There ought to be a glide path where you do not have a cliff that the House provides in 2020,” when the expansion of Medicaid under Obamacare is abruptly ended, said Senator Rob Portman of Ohio. But other Republicans said cutbacks were important to save taxpayer money. “The public wants every dime you can give them. Let’s face it, once you get them on the dole, they are going to take every dime they can. We’ve got to find some way of getting things under control, or this country and your future’s going to be gone,” said Republican Senator Orrin Hatch, a member of the healthcare working group. 