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WASHINGTON — Americans are increasingly doubtful Congress and the White House will reach a budget deal as the deadline to the “fiscal cliff’’ approaches, according to a new poll, though more said they still think a compromise eventually will be formed out of the fight.

According to Gallup, just half of those polled said they think President Obama and Congress are at least somewhat likely to reach a budget compromise, down from a high of 59 percent on Dec. 9. An increasing number, 48 percent, said they see no resolution before a deadline of Jan. 1.

The cliff, that self-imposed deadline set in place last year to force a deal on government expenditures and revenues, would institute broad spending cuts across government programs and allow President George W. Bush’s tax cuts to expire. Both Republicans and Democrats have offered evolving proposals on how to avoid both actions.

But as they have sparred back and forth, with House Speaker John Boehner’s “Plan B’’ proposal notably failing before the shutdown in Washington for the Christmas holiday, Obama and his allies appear to be coming out on top, at least in the court of public opinion as measured by Gallup.

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A majority of survey respondents — 54 percent — said they approve of the way Obama has handled the negotiations, and 45 percent said they approve of Democratic leaders in Congress. Just 26 percent said they approve of Boehner and the Republican congressional leadership.

That’s a sharp increase for Obama and the Democrats, 6 and 11 percentage points respectively, since Gallup’s last round of polling Dec. 15-16. Approval ratings for Boehner and the Republicans remained low, increasing by 1 point for the House speaker and decreasing by 3 points for his colleagues.

A majority of respondents, 68 percent to 22 percent, also said they favor compromise over strict adherence to principles in the budget negotiations.

Obama is scheduled to return to Washington on Thursday to restart negotiations, cutting short his holiday vacation to Hawaii. The House and Senate are reconvening after the holiday, though neither chamber has any specific legislation laid out on their schedules.

The poll was conducted between Dec. 21 and 22 via telephone interviews with 1,076 people, with a margin of error of plus or minus 4 percentage points.

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