President Donald Trump is wrong for wanting to change the Senate rules to eliminate the 60-vote threshold for most legislation, Sen. Jeff Flake, R-Ariz., told Monday's "CBS This Morning."

"That would be a big mistake," Flake said, because "We are at our best in the Senate when we work across the aisle."

To illustrate his point, Flake pointed out Obamacare was pushed through by only the Democrats, and now only Republicans are struggling to repeal it.

"I don't want to lurch back and forth every couple of years from one extreme to the other," Flake said. "Those rules are there for a reason. They're good . . . They invite us to work across the aisle, and we're better when we do that."

Flake, who on the show to promote his new book, "Conscience of a Conservative: A Rejection of Destructive Politics and a Return to Principle," said the GOP has lost its way during the Trump presidency.

"Being a conservative doesn't just mean that you adhere to conservative policy . . . it means you're conservative in comportment as well . . . In foreign policy, a conservative is nothing if he's not sober and measured," Flake said. "That matters in the White House . . . and I think we've lost that . . . because if you just have erratic behavior unmoored from principle, that's not a good combination."

Flake said he did support some of Trump's decisions, such as his Supreme Court appointment, regulatory policy, and his instincts on tax policy. But he stressed the president is, for example, "profoundly un-conservative" with his "protectionist attitude" toward free trade and isolationism.

Asked if he thinks Trump will support his bid for re-election, Flake said "that's up to him. Obviously, there are only 52 [GOP] senators. We have a small majority. But I think we've reached about the limits of what we can do just with our small majority. We've got to start reaching out across the aisle, [but] . . . That's not going to happen if you refer to the other party as my enemies, or losers, or clowns."

Flake said he kept the writing of his book a secret because he did not want to be talked out of it, saying "I think we have a crisis of principle, and we need to get back to what conservative really means."