Leading House moderate Charlie Dent of Pennsylvania complained that the final House measure passed May 4 was "haphazardly constructed and hastily considered."

He isn’t alone: Senate Republicans are already promising to carve it up and build a better version.

Woodruff said his Cancer Action Network plans to meet with members of the task force Senate Majority Leader Mitch McConnell helped assemble to lead his party’s efforts on the health bill.

The American Medical Association said in a letter to Senate leaders Monday that it’s ready to work with Congress on the bill, and that the measure shouldn’t weaken health coverage.

Health insurers will make their case to senators as well, an insurance lobbyist said. Republican senators like Rob Portman, who represents Ohio where Obamacare’s Medicaid expansion is popular, and Dean Heller, who could face a contentious re-election in the swing state of Nevada, may prove helpful to their cause.

Many conservative groups—including the Heritage Foundation, Club for Growth, Tea Party Patriots and FreedomWorks—were also left out of the House deliberations.

Trump’s Surprise

President Donald Trump expressed surprise when leaders of several of these groups told him during a meeting in March that GOP leaders hadn’t consulted them, according to several participants. Many ended up backing the bill days before it was passed, after some last-minute changes.

Edmund Haislmaier, a senior health policy research fellow at the Heritage Foundation, said he wasn’t consulted in the crafting of the House health bill, and he didn’t know anyone else in the policy community who was. He added that while it’s important to guard against lobbyists writing legislation in the interest of their clients, lawmakers need to consult industry players like insurance companies.

Many big insurers have largely dropped out of Obamacare markets after facing losses when premiums didn’t cover the cost of caring for consumers who signed up, and others that are still in the markets are proposing steep premium increases.