Story highlights Republican senators are finding it's not so easy to tackle the party's signature campaign issue

One issue: The lack of women in the 13-member health care plan group

Washington (CNN) It wasn't long after the House finally passed its bill to repeal and replace Obamacare that senators were already vowing to do it their way.

But in the week since, Senate Republicans are quickly coming up against some of the same obstacles that dogged House Republicans -- and dealing with new problems of their own creation.

Republican leaders have spent the early days of their Obamacare repeal effort pelted with questions about why they announced a 13-man working group last week that didn't include a single female senator.

"I would have recommended a little diversity there from a gender perspective," Sen. Tim Scott, a South Carolina Republican, told reporters Tuesday.

Throughout the health care debate in the House, Republican senators didn't shy away from criticizing the negotiations happening across the Capitol. More than one senator warned that policies in the House were dead on arrival in the Senate. Kentucky Sen. Rand Paul led the press corps in a search for the bill he accused House leaders of keeping under lock and key even from members of the Republican Party. And, just after the House bill was passed, Sen. Lindsey Graham tweeted that it should be viewed with extra "caution" having been finalized the night before.

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