In fact, the last time a Democratic presidential candidate won a majority of white voters was in 1964 -and race has a LOT to do with this pattern. In 1860 the Northern states where slavery was abolished voted solidly for Abraham Lincoln, the Republican candidate. The Democratic Party had splintered between Northern and Southern interests into the National (Northern) Democratic Party and Constitutional (Southern) Democratic Party. A fourth party, the Whig Party, had been a strong force in US politics for two decades but had dissolved. Some former Whigs formed a new fourth party, the Constitutional Union Party, that also ran in the 1860 presidential election.
The Southern slave states voted overwhelmingly for the Southern faction of Democrats or the Constitutional Union Party. Only Missouri voted for the Northern faction of the Democrats. The united Republicans in the North successfully elected Lincoln to the White House in 1860. By April of the next year the US was embroiled in its civil war.
After the Civil War, a basic pattern emerged where the North voted primarily Republican and the "Solid South" supported Democrats overwhelmingly. In 1964, President Lyndon Johnson, a Southern Democrat from Texas, signed the Civil Rights Act into law. This law ensured American adults regardless of race could vote. When he signed the law, Johnson pondered that he might be handing the South over to the Republicans. Sure enough, white voters revolted. Since the Civil Rights Act was signed into law, former Dixiecrats have moved en masse to the Republican Party. No Democratic presidential candidate has broken 50% of the the white vote since 1964 -though Carter, a Southerner, almost did with 48% of the white vote in 1976.
Today the party patterns have largely flipped with the Old South a Republican stronghold in terms of national politics. Likewise, New England moderate Republicans are all but extinct with the former Union states largely voting Democratic in national elections.
You can compare white male voters' outcomes above to the outcomes for each state for the whole population of voters below: