Maryland's Republican Gov. Larry Hogan says that while President Trump is likely to fend off a GOP primary challenger, he may be vulnerable in the general election against the eventual Democratic nominee.

"The issue I'm concerned about is he has a very low re-elect number, I think in the 30s, high 30s, low 40s," Hogan said of Mr. Trump's poll numbers in an exclusive interview with CBS News Tuesday. "So the chance of him losing a general election are pretty good. I'm not saying he couldn't win but he's pretty weak in the general election."

If the president's approval ratings continue to dip heading into the campaign cycle, Hogan said the Republican Party will need to consider what his potential defeat next November could mean for GOP office holders across the country.

Get updates from the campaign trail delivered to your inbox

"At some point if he weakens further, Republicans would say we're concerned about whether or not he's going to win if we're going to face a very far-left Democratic nominee, and is he going to take the rest of us down with him if you're an elected official," he added.

Hogan easily won re-election in November by double digits, defeating former NAACP president Ben Jealous. But attempts by Republicans to win more seats in the state legislature fell short and GOP incumbents lost three key county executive races in part due to statewide opposition to Mr. Trump.

Republicans opposed to some of Mr. Trump's policies and style of governance have been courting Hogan, a popular two-term Republican governor in a deep-blue state, to launch a White House bid and challenge the president for the GOP nomination.

Hogan told CBS News the probability of someone stealing a party's presidential nomination from an incumbent president is very slim. But then, he noted that the odds were also not in his favor when he won two consecutive gubernatorial races in Maryland.

"I don't know what it's going to look like down the road," he said. "Today it would be very difficult. Nobody has successfully challenged a sitting president in the same party in a primary since 1884. I know I'm the second Republican in the history of Maryland but I'm not sure, that's probably about the same odds I guess."

Hogan shares more about his own potential presidential ambitions Wednesday on "CBS This Morning."