But Democrats view the coming Buffett Rule vote as fitting into a theme of “fairness” for the middle class at a time when most Americans see a society tilted in favor of a wealthy elite. An Associated Press/GfK poll in February found that 65 percent favor a law requiring all Americans with incomes of $1 million or more to pay at least 30 percent in taxes. Only 26 percent opposed.

White House officials will target senators in 13 states with media outreach efforts, while Obama campaign volunteers try to raise the heat.

“This is one of those issues where if the American people are watching, our chances of winning the vote are dramatically improved,” said Senator Sheldon Whitehouse, Democrat of Rhode Island and the author of the Buffett Rule bill. “If people can vote in the dark, the special interests that support the loophole have a much, much better chance of holding on.”