By DAVID M. HERSZENHORN, The American Cancer Society sounded an alarm Friday about a small change in wording in the Senate health care bill

that could have big implications for people with cancer and other chronic diseases that require expensive treatment. 

And the White House quickly said it would help.

Language in earlier versions of the Senate bill and in the bill adopted by the House last month would eventually bar insurance companies from setting annual limits on benefits, and they would immediately bar caps on lifetime limits.

But the latest Senate proposal, pulled together by the majority leader, Harry Reid, Democrat of Nevada, allows annual limits — on the condition that they are not “unreasonable.” The federal government would define “unreasonable.” The bill does not.

Senate leaders and the White House quickly said they would adjust the bill.

“The President has made it clear that health insurance reform legislation should prevent insurance companies from placing annual limits on health expenditures that can force families into financial ruin,” Reid Cherlin, a White House spokesman said Friday. “We will continue to work with Congress on this policy.”

The cancer society, in a statement, said, “We are confident that our concerns will be resolved.”