President Donald Trump's restraint Wednesday morning on Twitter allowed the stock market to absorb the Cohen-Manafort bombshells in stride, said veteran trader Art Cashin.

The reaction on Wall Street was "amazingly benign," the UBS director of floor operations at the NYSE, told CNBC's "Squawk on the Street." "But I think that's because the [tweets] from the president have been amazingly benign given his past history."

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Late Tuesday, former Trump lawyer Michael Cohen pleaded guilty to federal fraud charges in New York as ex-Trump campaign chairman Paul Manafort was convicted of fraud by a federal jury in Virginia.

The sentiment in the stock market — which seems to care more about a stronger economy than Trump's legal troubles — could swing if Democrats are able to win a majority in the House in the November elections, Cashin said.

Some Democrats have already started to rumble about impeachment. (If the House were to decide to impeach a president, the Senate must then vote to convict or acquit.)

"I don't think [Trump] will ever by fully impeached," Cashin said, but he warned that such proceedings, if pursued, could tie up the federal government for years. "For now, it's watchful waiting."

"The market would be a little concerned if they thought the progress that we're making on deregulation and things like that were to suddenly dry up because the government becomes paralyzed with introspection," he said.

Cashin said it's hard to draw any parallels on market reaction to the Bill Clinton and Richard Nixon situations because the political and economic environments were so different.

On Dec. 19, 1998, President Clinton was impeached by the House on charges of lying under oath about the Monica Lewinsky affair. Clinton was acquitted by the Senate.

Nixon decided to resign as president in August 1974 as impeachment proceedings were underway.