Economists say that when claims drop consistently below 375,000 that job creation is hitting a fast enough pace to lower the unemployment rate.
A Friday report could show that the economy added around 162,000 jobs in April.
Job creation had been strengthening since September as weekly and monthly claims posted steady improvement.
But in the past month, the economy has posted mostly disappointing jobs data, adding only 120,000 jobs in March down from an average of more than 200,000 from December through February.
Meanwhile, the unemployment rate fell to 8.2 percent in March, but mostly because potential workers gave up their search for jobs.
Workers need jobs to help boost consumer spending, which represents 70 percent of economic activity.