The highest consumer confidence reading in more than 16 years and the postelection stock market rally may not translate into more robust economic growth, former Clinton Treasury Secretary Larry Summers told CNBC on Thursday.

"If you use the standard of what the administration has held out the hope for, 3 to 4 percent growth, there is nothing in any data suggesting we're moving towards that 3 to 4 percent growth standard," Summers said on "Squawk Box."

Summers, also a former economic advisor during Barack Obama's presidency, reiterated concerns that optimism for faster economic growth due to President Donald Trump's promised agenda of tax cuts and deregulation might be a "sugar high."

"We may be seeing a kind of sugar high, and sugar highs tend to be followed by much less happy periods," warned Summers, president emeritus of Harvard University.

"If you continue to have the degree of division, confusion, rancor and uncertainty in Washington that we've seen, we may not see those sentiment changes last as long as many people thought they would a couple months ago," Summers said.

The Republican Party's "stunning" lack of unity on repealing and replacing Obamacare undermines Trump's entire agenda, he argued.

"I would be cautious about any big revision to the upside in forecasts" for economic growth, Summers said, also partly due to the Federal Reserve's desire to prevent the economy from overheating. The Fed already put one interest rate hike on the board for 2017 earlier this month. Two or three more rate increases this year are being debated in the markets.

