Julie Arkison remembers what it was like to buy health insurance before the Affordable Care Act created standards for coverage. The policy she had was from the same insurer that covers her now, but it did not pay for doctor visits, except for a yearly checkup and gynecological exam.

“I couldn’t even go to my regular doctor when was I sick,” said Ms. Arkison, 53, a self-employed horseback-riding teacher in Saline, Mich.

The plan did not cover her exams before and after hip surgery, her physical therapy after her operation, the crutches she needed while she recovered, or any of her medications. She estimates that she spent $20,000 on medical care in the seven years before she could buy a plan through the marketplaces created by the Affordable Care Act.

As Senate Republican leaders struggle to secure enough votes to repeal and replace the health law, the centerpiece of their effort to win conservative support is a provision that would allow insurers to sell such bare-bones plans again. The new version of the bill released on Thursday incorporates an idea from Senator Ted Cruz of Texas that would permit insurers to market all types of plans as long as they offer ones that comply with Affordable Care Act standards. The measure would also allow companies to take into account people’s health status in determining whether to insure them and at what price.