The CBO on Monday scored the Senate bill, released on Thursday after weeks of secrecy. It would reduce the U.S. deficit by some $200 billion more over a decade than the plan that passed the House in May, while the projected insurance-premium hikes are steep rather than stratospheric. But they would still be painful for lower and middle-income individuals. For example, a 64-year-old making $26,500 a year would see an increase of more than 280 percent to $6,500 a year by 2026, the CBO said.

Before the CBO's score came out, the White House sought to further undermine the office by saying it has a poor track record in healthcare projections, having overstated the early take-up of coverage under President Barack Obama's Affordable Care Act. Yet the CBO is broadly nonpartisan and, importantly, it's consistent in how it evaluates legislation, so its analysis carries weight.

Four conservative Republicans have already said they can't support the current bill, largely because it doesn’t go far enough in repealing Obamacare. Senator Ron Johnson of Wisconsin, who wrote a commentary on Monday opposing the plan, said the bill would fail if the chamber voted to proceed on Tuesday.

Moderates are also unhappy. Roughly in line with the House bill, under the Senate version Washington would spend around $800 million less over 10 years on Medicaid – healthcare for lower-income Americans – than under current law, according to the CBO, with 15 million fewer enrolled in the program. Senator Dean Heller of Nevada, as one example, opposes ending the expansion of Medicaid under Obamacare, which his state and dozens of others adopted.

Republicans have pledged for years that they would repeal Obamacare but they have a slim 52-member majority in the 100-member Senate. Changes that appease conservatives might alienate centrists, and vice versa. The GOP leadership will need both heart and head to pass any form of repeal.