WASHINGTON — Public campaigning gave way to the privacy of the voting booth Tuesday with control of the Senate, the makeup of the House and three dozen governorships at stake.

President Barack Obama, his approval ratings low, was not on the ballot midway through his second term. But even he said his policies were, and Republicans rushed to agree.

“The president’s policies have just flat-out failed,” House Speaker John Boehner said Monday, campaigning for a 13th term in Congress and hoping for two more years as top House leader. He and other Republicans vowed to change Obama’s policies, but have offered little in the way of specifics.

Democrats didn’t so much defend the president as insist they were independent of him.

“There are two people on the ballot tomorrow, me and Scott Brown,” Sen. Jeanne Shaheen of New Hampshire said as she made the rounds of six campaign stops on the race’s final full day.

The main prize in a $4 billion campaign was control of the Senate, a contest that sprawled across three dozen states and spawned attack ads beyond counting.

A large number of competitive races combined with the possibility of runoffs in Louisiana and Georgia meant that neither party might be able to claim victory by the day after Election Day.

About 10 Senate races drew most of the attention.

In Kentucky, Senate Republican leader Mitch McConnell squared off with Democrat Alison Lundergan Grimes in a race that cost more than $50 million and was relentlessly negative.

Democratic retirements gave Republicans their best pickup opportunities in Montana, South Dakota and West Virginia, where Rep. Shelly Moore Capito hopes to become the first member of her party to win a Senate seat in more than a half-century.

Another Democratic retirement produced a highly competitive race in Iowa between Republican Joni Ernst and Democratic Rep. Bruce Braley.

A Republican retirement in Georgia led to one of the country’s most closely-watched races, between Democrat Michelle Nunn and Republican businessman David Perdue.

Democratic incumbents in states that Obama lost in 2012, including Alaska, Arkansas, Louisiana and North Carolina, faced strong challenges. The same was true in states the president won two years ago, Colorado and New Hampshire.

The wildest wild card of all was Kansas, where 78-year-old Republican Sen. Pat Roberts is in a competitive race with independent Greg Orman.

Republicans expressed optimism about their overall chances to win control of the Senate, while Democrats countered that a costly get-out-the-vote program to encourage millions of blacks, young voters and women to vote could save their majority.

The spreading popularity of early voting produced the equivalent of an election within an election.

Early voting topped 18 million ballots in 32 states, and both parties seized on the number as evidence of their own strength.