In a flood of lawsuits, Roman Catholics, evangelicals and Mennonites are challenging a provision in the new health care law that requires employers to cover birth control in employee health plans — a high-stakes clash between religious freedom and health care access that appears headed to the Supreme Court.

In recent months, federal courts have seen dozens of lawsuits brought not only by religious institutions like Catholic dioceses but also by private employers ranging from a pizza mogul to produce transporters who say the government is forcing them to violate core tenets of their faith. Some have been turned away by judges convinced that access to contraception is a vital health need and a compelling state interest. Others have been told that their beliefs appear to outweigh any state interest and that they may hold off complying with the law until their cases have been judged. New suits are filed nearly weekly.

“This is highly likely to end up at the Supreme Court,” said Douglas Laycock, a law professor at the University of Virginia and one of the country’s top scholars on church-state conflicts. “There are so many cases, and we are already getting strong disagreements among the circuit courts.”

President Obama’s health care law, known as the Affordable Care Act, was the most fought-over piece of legislation in his first term and was the focus of a highly contentious Supreme Court decision last year that found it to be constitutional.