The failure calls into question whether Trump and GOP leaders in Congress can deliver on the pro-economic growth promises that have supported the stock market and buoyed business and consumer sentiment, Summers argued on CNBC's "Squawk Box."
Summers, a former economic advisor to President Barack Obama, also said he's concerned that a fight over funding Planned Parenthood could lead to a government shutdown. House Speaker Paul Ryan suggested earlier this week the House would not try to defund Planned Parenthood while working to approve spending to keep the government open beyond April 28.
Couple fiscal uncertainty with questions about Russia's interference in the 2016 election, and there are potential pitfalls on multiple fronts, said Summers, president emeritus of Harvard University.
"There's a huge set of leadership issues around the president's ability to lead in the way presidents do that comes before, and is separate from, whatever add-on you get from Russia investigations," Summers said.
On Thursday, Russian President Vladimir Putin denied accusations that Moscow meddled in U.S. elections. During a panel moderated by CNBC, Putin said, "All those things are fictional, illusory and provocations, lies."