The two men battling for the north country’s congressional seat spent Thursday trying to prove or disprove an elemental notion in the race: that the Republican challenger is within striking distance of taking out the incumbent Democrat.

The campaigns of Republican Matthew A. Doheny of Watertown and Rep. William L. Owens, D-Plattsburgh, are both claiming the advantage. “I have very good news: we’re in a statistical dead heat with our opponent,” Doheny campaign manager Jeff Freeland said in an email to supporters with the subject line, “We’re Close.”

Said Owens campaign manager James Hannaway in an email: “We’ll keep meeting with folks and travelling around the district, talking about how Bill is working for jobs on Main Street. After all, the only poll that matters is the one on Election Day.”

The Doheny campaign released an internal poll Wednesday that showed Mr. Owens leading, 45 percent to 40 percent, among likely voters. The margin of error was 5 percent. Though he’s behind in his own poll, it’s not by much.

But that wasn’t the end of it. The Owens campaign released a poll of its own, showing Mr. Owens leading 50 percent to 36 percent. The margin of error was also 5 percent. It also showed Mr. Obama leading Mr. Romney, 51 percent to 39 percent.

The Owens poll was similar to a previous internal poll released by Democrats, and an independent Siena College Research Institute poll.

Both campaigns spent much of Thursday behind the scenes trying to convince reporters that their own survey reflected reality.

“It’s an impossibility,” Mr. Doheny said of the Owens poll.

While it’s technically true that the only poll that will decide who goes to Congress is the one on Nov. 6, perception matters. Candidates who are seen as down big might start to lose support among potential donors. Events on Wednesday and Thursday may have helped alter the trajectory of the race, but conflicting evidence makes it impossible to deduce where it stands today.

For example, on Wednesday night, pundits on both the left and right gave Republican presidential candidate Mitt Romney the advantage over President Obama in the first presidential debate. And in politics, a rising tide can lift all ships in the flotilla.

“If you look at how things start to shake out, of course Mitt Romney having better support is going to help,” said Robert Blizzard, a pollster for Mr. Doheny whose firm, Public Opinion Strategies, also does work for Mr. Romney.

Mr. Romney’s decline in the polls risked cutting short his coattails. The Republican and conservative base in the north country might not show up in droves at the polls if the man on the top of the ticket was getting pummeled.

But his debate performance could help stop, if not reverse, that slide, Mr. Blizzard suggested.

Other tea leaves are less scientific, but could be instructive. For example, the U.S. Chamber of Commerce will soon begin airing a television advertisement that assails Mr. Owens for his vote to approve the Affordable Care Act. The Doheny campaign argues that groups like the Chamber of Commerce wouldn’t invest money against an incumbent if they thought he was up by 14 points. Other outside groups have continued to pour money into the district, including the National Republican Congressional Committee, the campaign arm for House Republicans.

But as far as many in the national media are concerned, Mr. Owens is favored. The race is rarely mentioned in major publications’ round-ups of the top competitive races, though it sometimes is. It was moved from the 37th most competitive to the 44th most competitive out of 435 House races nationally. The New York Times wrote Thursday that Mr. Owens has “managed to maintain an advantage in the race.”

Also on Thursday, Roll Call, a Washington, D.C. publication, moved the race from its “tossup” category, meaning that the chances were roughly equal, to “leans Democratic,” meaning Mr. Owens is slightly favored.

Wrote Roll Call: “Democrats who, earlier this cycle, thought the incumbent was done are now feeling pretty confident on this race.”

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