The Supreme Court appeared closely divided Wednesday during heated arguments over President Obama’s health care law, but questions from Justice Anthony Kennedy gave proponents hope the statute will be upheld. At least four justices appeared skeptical about a challenge to the law that could eliminate tax credits used by millions of Americans to pay insurance premiums. That could leave 34 states with unmanageable insurance markets featuring rising premiums and millions more residents uninsured.

The principal argument advanced by the law’s opponents — that four words in the 906-page statute permit the use of tax credits only in states that set up their own health insurance exchanges — appeared to please the court’s most conservative members.