WASHINGTON—President Obama Wednesday threatened to veto House Speaker John Boehner’s backup measure to prevent income taxes from rising for all Americans except those earning more than $1 million a year, part of political skirmishing that is casting a shadow over negotiations on the fiscal cliff.

``The deficit reduction is minimal, and perversely, given its authors, solely through tax increases with no spending cuts,’’ White House communications director Dan Pfeiffer said in a written statement. ``This approach does not meet the test of balance, and the President would veto the legislation in the unlikely event of its passage.’’

Boehner said Tuesday he would push his bill as a ``Plan B’’ backup to avert tax hikes on most Americans in the event negotiations to avert the fiscal cliff break down. The measure would give the House GOP some political cover in the event the fiscal cliff is reached on Jan. 1 and Bush-era tax cuts expire as scheduled. Polls show that most Americans would blame Republicans if the fiscal-cliff is reached without a solution, a situation that would risk a recession with $500 in combined tax hikes and government spending reductions.

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Senate Democrats have vowed to vote against the proposed House Republican bill and its $1 million threshold. They have already approved a bill that would extend tax cuts for 98 percent of Americans whjile allowing tax rates to rise for families making more than $250,000

It is not yet clear that Boehner even can win passage of his bill in the House, because some more conservative members of his caucus have expressed opposition to a measure allowing taxes to rise for anyone. These conservatives are holding out for a bill that extends the tax cuts for all taxpayers, from the poor to the middle class to the very wealthy.

The dynamics help illustrate one of the dilemmas for Boehner: with many in his caucus entrenched against tax increases, he will need a coalition of House Democrats and Republicans to win passage of any broader compromise that he negotiates with Obama. But forging such a compromise could cost him his gavel if a majority of Republicans decide to reject his leadership for accepting tax increases.

The negative rhetorical tone marks a shift after both sides appeared to be making progress in negotiations over the weekend and on Monday. The White House said Boehner’s Plan B would only cut $300 billion from the deficit, through increased revenues from millionaires.

Boehner spokesman Brendan Buck issued a response to Obama’s veto threat: “The White House’s opposition to a back-up plan to ensure taxes don’t rise on American families is growing more bizarre and irrational by the day. Republicans have always said a broader, ‘balanced’ plan is the ideal solution, and we have put one forward. In the absence of a ‘balanced’ solution from the President, however, we must act to stop taxes from rising across the board in 12 days.’’