President Donald Trump is set to make a prime-time television address on Afghanistan on Monday – and the big question is whether he can give a "thoughtful, grown-up president's speech" or will he ad-lib, Republican strategist Mike Murphy told CNBC.

"It's kind of a high-stakes moment. They badly need a functional presidency to reassure markets and everybody else that they can operate and move onto important policy things that Republicans want to try to get done, which are very hard to do politically," Murphy said in an interview with "Power Lunch" on Monday.

Trump is expected to lay out his long-awaited U.S. strategy for the war in Afghanistan at 9 p.m. ET on Monday. The speech comes after a particularly bruising week in which he was widely criticized for blaming both white nationalists and counterprotesters for violence at a Virginia rally this month organized by neo-Nazis and white supremacists.

"There's no doubt they want to change the narrative," Murphy said of the Trump administration.

He said Trump needs to be careful about overpromising.

"Less is more when promising things in a quagmire like Afghanistan. The president doesn't like to operate that way. I think he's going to have to be very careful about setting expectations tonight," said Murphy, a former advisor to Jeb Bush, Mitt Romney and John McCain.

— Reuters contributed to this report.