Before the strong December jobs report was released, the odds were already low for an interest rate cut in the next Federal Reserve decision on January 29.

The surprising 256,000 increase in new jobs in December and a declining unemployment rate is good news, but the latest employment reports masks recent softness in the labor market. The increase in new jobs in December, for example, was centered on just four industries: Health care, government, retail and leisure and hospitality.

A red-hot jobs report means that interest rate cuts aren't coming, and cuts could be next. Here's what strategists say is next for rates and stocks.