WASHINGTON -- Republicans are preparing an alternative health-care bill to Democratic legislation, House Republican Leader John Boehner said, marking a shift in strategy as the full House is set to begin debate on the issue this week.

Boehner said Sunday the Republican bill would extend health-insurance coverage to "millions" of Americans but wouldn't try to match the scope of the House Democratic bill unveiled last week. The Democratic legislation, if passed, is estimated to expand coverage to more than 30 million Americans now without insurance. Its estimated gross cost is $1.055 trillion over 10 years.

"What we do is we try to make the current system work better," Boehner, of Ohio, said on CNN's "State of the Nation." The GOP plan would likely be less costly to taxpayers and involve less government intrusion into the private sector. Boehner said the bill would take "a step-by-step approach" to expanding coverage...