On Sunday, Trump blamed the Tennessee Republican for the Obama administration's nuclear deal with Iran. He also suggested that Corker actively pursued a re-election endorsement from Trump and a top-ranking Cabinet post.
In response, Corker blasted the White House, tweeting that it had become an "adult day care center" and saying that someone "missed their shift."
"I do think it makes it somewhat more difficult," Cashin, UBS director of floor operations at the New York Stock Exchange, said in an interview on "Squawk on the Street." "But we never have a weekend without a surprise out of Washington."
"This market — the rally — has been living on hope and the hope is you'll actually get something done in Washington," Cashin said. "It's hard to believe. They look they couldn't agree on what time of day it is."
Stocks were little changed Monday. The Nasdaq composite hit a record high and the Dow Jones industrial average also posted an all-time high.
Cashin said Monday's session has a "15 percent chance of being the slowest full trading day of the year" as the bond market and banks shut down for the Columbus Day holiday. "You also have a holiday in Tokyo and you have another one in Korea," he said.
This week investors will focus on the early portion of earnings season, Cashin said. Later in the week, the season gets underway with reports from BlackRock, Delta Air Lines, JPMorgan Chase, Bank of America and Wells Fargo.
They'll also be focused "again on the circus in Washington," Cashin said. "We'll see if we can get past the clowns and get into something more serious."