WASHINGTON — As early voting began Monday in Florida, Senator Bill Nelson and Andrew Gillum, who is running for governor, had former Vice President Joseph R. Biden Jr. come to Jacksonville and Tampa to urge Democrats to go to the polls in what are two of the most hard-fought races in the country.

Early voting also started Monday in Texas, and that’s where President Trump spoke in an 18,000-seat N.B.A. arena. But he was rallying support in a pair of less-competitive races: the re-election campaigns of Senator Ted Cruz and Gov. Greg Abbott.

Conspicuously absent from the raucous festivities at Houston’s Toyota Center, where thousands also congregated outside, was the local Republican congressman who is locked in a difficult campaign: John Culberson, whose well-heeled district is full of moderates who recoil from Mr. Trump.

The split-screen between Florida and Texas — one the most crucial presidential battleground in the country, the other a pillar of conservative strength — neatly illustrated Mr. Trump’s role in the fall campaign. He is often away from the center of action, shunned by many of his party’s most vulnerable House candidates but still commands enthusiastic audiences on a scale rarely seen in a midterm election.