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President Obama brushed off criticism over his administration's inaccurate reporting on job creation Wednesday, telling Fox News the accounting is an "inexact science" and that any errors are a "side issue" when compared with the goal of turning the economy around. He said job growth is his No.1 responsibility.

The president was responding to criticism from Republicans, as well as Democratic Rep. David Obey, who drew attention to embarrassing errors on the Recovery.gov Web site that tracks stimulus funding. The site is under fire for claiming a number of jobs were created from the stimulus in congressional districts that don't exist and accepting unrealistic and inflated jobs data from various sources.

Obama said he understood the "frustration" but said his focus has to be on accelerating job growth.

"I think this is an inexact science. We're talking about a multitrillion-dollar economy that went through the worst economic crisis since 1933. The first measure of success of the economic recovery is, did we pull ourselves back from the brink? We did," Obama said. "The question now is, can we make sure we're accelerating job growth? That's my No. 1 job. Nobody's been more disappointed than I have to see how high the unemployment rate has gotten. And I spend every waking hour, when I'm talking to my economic team, about how we are going to put people back to work."

Obama spoke with Fox News' Major Garrett in Beijing, in the middle of his tour through several Asian countries. Economic issues have inevitably been on the front burner during the president's leg in China, which is the United States' biggest government lender.

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In the interview, Obama spoke candidly about the precarious balancing act his administration is trying to perform. He wants to spend money to kick-start the economy, but at the same time is in danger of creating too much red ink. Obama warned Wednesday that the United States' climbing national debt could even drag the country into a "double-dip recession," though he said he's still considering additional tax incentives for businesses to reverse the rising unemployment rate.

"There may be some tax provisions that can encourage businesses to hire sooner rather than sitting on the sidelines. So we're taking a look at those," Obama said. "I think it is important, though, to recognize if we keep on adding to the debt, even in the midst of this recovery, that at some point, people could lose confidence in the U.S. economy in a way that could actually lead to a double-dip recession."

The warning was a rare admission from the president that the economy is still at risk of turning back -- consumer confidence fell unexpectedly in September and unemployment is at 10.2 percent. Such a recession repeat, following a relatively brief recovery period, could be politically devastating for Obama, let alone economically devastating for the country. The president said Wednesday that striking the right balance is one of the "trickiest" tasks facing his administration -- "to on the one hand make sure the recovery is supported and not withdraw a lot of money either with tax increases or big spending cuts."

"It's about as hard of a play as there is," Obama said.

He said any additional jobs-stimulating legislation will have to "fit into that broader framework," but he would not make a pledge that such a bill would not increase the deficit.

The president also weighed in very directly on a controversial amendment to pending health care legislation, which he's still trying to get passed before the end of the year. After the House passed its bill with a measure authored by Rep. Bart Stupak, D-Mich., to restrict federal subsidies from going toward practically any abortion coverage, Obama signaled that he wants that watered down.

"There is a balance to be achieved that is consistent with the Hyde Amendment (which bars federal funding from covering abortion) ... I believe in the basic idea that federal dollars shouldn't pay for abortions. But I also think we shouldn't restrict women's choices, so I think there's some negotiations going on, not just on the Democratic side, but I think among people of good will on both sides, to see if we can arrive at something that meets that criteria. And I'm confident we can do that."

Asked if Stupak's amendment strikes that balance, he said: "Not yet."

Countless deadlines in the health care reform legislative process have been missed since Obama took office. There have been conflicting signals out of Capitol Hill over whether Congress can even get a bill to the president's desk by the end of the year.

Obama told Fox News that much of the delay stems from the amount of time it takes for Congress to receive cost estimates, and that it's "entirely appropriate" for legislators to wait on that. But he said he's still pushing for a successful bill by year's end.

"I want this done as soon as possible," Obama said. "We are pushing and prodding as hard as we can."

Health care reform and jobs are just two of a slew of high-priority items Obama has tried to tackle in his first year in office. His trip to Asia came in the middle of a tense and drawn-out decision-making process over strategy in the Afghanistan war; controversy over the handling of Guantanamo Bay inmates, and new and potentially disruptive developments between the Israelis and Palestinians.

Obama took a stern tone toward Israel during the interview with Fox News, calling it "dangerous" that the country plans to add 900 new apartments to an existing Jewish settlement in East Jerusalem -- an area Palestinians hope to claim as their capital absent a peace agreement with Israel.

Israeli Prime Minister Benjamin Netanyahu said Tuesday that building permits were permitted for construction in Gilo for what would be upscale dwellings in the lower-middle class neighborhood.

"The situation in the Middle East is very difficult, and I've said repeatedly and I'll say again, Israel's security is a vital national interest to the United States, and we will make sure they are secure," Obama told Fox News.

"I think that additional settlement building does not contribute to Israel's security. I think it makes it harder for them to make peace with their neighbors. I think it embitters the Palestinians in a way that could end up being very dangerous," he added.

The U.S. administration has roundly criticized the decision to expand the settlement, a point of bitter contention for Palestinians who wish to make the Old City of Jerusalem as well as other sites holy to Jews, Muslims and Christians as part of its capital.

That vision is part of a roadmap to a two-state solution that the Palestinians this week have abandoned in hopes of getting pre-emptive U.N. approval for a state that includes East Jerusalem as its capital as well as the West Bank and Gaza.

Obama also said Wednesday that he still plans to close the Guantanamo Bay detention camp next year even though his administration is widely expected to miss its self-imposed January 2010 deadline for shuttering the Cuba facility.

"We are on a path and a process where I would anticipate that Guantanamo will be closed next year," he said. "I'm not going to set an exact date because a lot of this is also going to depend upon cooperation from Congress."

And despite the criticism he's faced for spending nearly three months deliberating over whether to grant Gen. Stanely McChrystal's request for more troops in Afghanistan, Obama told Fox News that the backlash from both sides ranks as some of the most valuable dissent he's heard so far.

"If I was just hearing one side, then I would probably not be getting the full reality of what's going on in Afghanistan," Obama said. "If I was just listening to hawks or doves on either side of the debate, then I probably wouldn't be making a very good decision."

The president briefly addressed how he views the government's role with respect to General Motors. He said that despite the federal government's massive stake in GM, his administration will not weigh in on the possibility that GM could direct bailout funds toward its European Opel unit.

"We are not going to meddle in GM's decisions," Obama said. "We are a shareholder but we are not an active shareholder. We have specifically said that we are not in the business of running a car company. We're not getting involved in day-to-day management."

He said the Detroit automaker owes the U.S. government money, but that "we want to get out of that business as soon as possible" and encourage repayment.

From China, the president was heading to South Korea for more high-level talks.

Obama told Fox News that he will speak to South Korean President Lee Myung-bak, whom he will hold a summit with on Thursday, about the pending trade agreement between the two countries but stopped short of committing to closing the deal next year.

"Well, the question is whether we can get it done in the beginning of 2010, whether we can get it done at the end of 2010," he said. "There's still some details that need to be worked out. Overall I think it's a potential good deal for U.S. exporters. But there's certain sectors of the economy that aren't dealt with as effectively and that's something that I'm going to be talking to "President Lee about."