According to data from the St. Louis Fed, the 10-year break-even inflation rate, which measures expected inflation derived from the U.S. 10-year treasury note yield and the treasury inflation-protected securities yield, fell to 1.66 percent on Friday, its lowest level since March. The 10-year yield rose more than 3 percent Monday to 2.23.
The Federal Reserve has a target inflation of 2 percent.
"If you look at the underlying inflation expectations data, which is really being driven by oil prices, I really would not suggest they need to do anything in a hurry," he said.
Further declines in oil prices could derail the Fed's plan for a rate hike before the year end, Burkly said.
"It's going to make it much more challenging for the Fed to say that there's an inflation problem, or that inflation is getting closer to their 2 percent target," he said.
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Burkly said the Fed may choose to raise rates regardless of the inflation target.
"I think they are on a pre-determined course that they want to get away from zero. So they're likely to do something in September or December," he said.
However, Craig Johnson, technical analyst at Piper Jaffray, said oil is on the verge of drop even further. He said if crude oil breaks through the $42 level, it could drop to the low $30 range.
"You've got people that are still bullish on oil trying to defend that level in here right now," Johnson said. "But it looks like it's going to peter out a little bit. In the next couple of days, if we start moving back below that level, you'll start a whole other leg lower."
Crude oil fell in early morning trading Monday before rallying and closing up more than 2 percent. The commodity has fallen more than 15 percent year-to-date.