It's not clear yet what the reaction will be from state Democrats to Tomblin's similar remarks.
After Manchin's remarks to the National Journal, Obama chief political adviser David Axelrod told CNN Manchin was concerned chiefly with his own political well-being.
"It's going to be a tough state for us again, and he's making a political judgment about himself," Axelrod said. "I would hope that the country's interests will enter into it as well, and that ultimately he will be supporting the president."
Obama is expected to do poorly in West Virginia.
The chief policy albatrosses from the Obama White House for West Virginia Democrats are environmental regulations targeting the coal industry, particularly regulations to curb mountaintop removal mining and emissions from coal-fired power plants. There is also the national health care reform law, which publicly available polling has found to be unpopular in the state.
Tomblin and Manchin have both stridently objected to the environmental regulations, although Tomblin has not taken up Republican Bill Maloney's challenge and called for the head of the U.S. Environmental Protection Agency to resign.
On health care, both men have hedged their bets.
The big question for the fall for both Manchin and Tomblin is whether Republicans can use Obama against either of them. So far, it hasn't worked to defeat either Manchin or Tomblin, and both men are facing Republicans they have previously defeated.
John Raese, Manchin's Republican challenger this year, failed to defeat Manchin using Obama in the special 2010 Senate election. Maloney also failed to defeat Tomblin by tying him to Obama in 2011's special gubernatorial election, although that election was decided by fewer than 8,000 votes.