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Mitt Romney carries newfound competitiveness in trust to handle international issues into the final presidential debate, combined with his highest personal popularity of the 2012 campaign. But continued weakness in his perceived economic priorities is keeping the race a close one.

Among other shifts, after last week's second debate, which included a spirited exchange on women in the workplace, the contest now has its largest gender gap of the season - a 14-point lead for Barack Obama among women, vs. a 12-point advantage for Romney among men.

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The result, as in previous ABC News/Washington Post polls since late summer, is essentially a dead heat between the candidates overall. In the first of what will be daily ABC/Post tracking polls for the rest of the contest, 49 percent of likely voters back Obama, 48 percent Romney.

See PDF with full results and charts here.

With tonight's debate focused on foreign policy, the poll, produced for ABC by Langer Research Associates, finds Romney virtually tied with Obama in trust to handle international affairs (49-46 percent, Obama-Romney) and terrorism (47-46 percent), as well as to serve as commander-in-chief of the armed services (48-45 percent). That reflects a shift in Romney's favor; Obama led on terrorism by 11 points as recently as Sept. 29, and on international affairs by 7 points earlier this month.

In another milestone for Romney, 50 percent of likely voters express a favorable opinion of him overall, while 47 percent see him unfavorably - his highest popularity score of the season, and one of the rare times he's been numerically above water in this measure. His personal popularity now roughly matches Obama's 52-46 percent, favorable-unfavorable.

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While more pick Obama as winner of the second debate, these advances for Romney appear to reflect a carry-over effect of his first debate performance. Overall, 37 percent of likely voters say their opinion of Romney has improved as a result of the two debates, double the 19 percent who think less of him. Obama gets just an even split, 15 percent to 18 percent, better-worse. (The rest say the debates haven't changed their views of the candidates - 65 percent in Obama's case, 43 percent in Romney's).

Still, Obama clawed back some ground in the second debate - he's seen as having won it by 48-29 percent, compared with Romney's 71-17 percent in the first debate. And the number of likely voters with a better opinion of Obama as a result of the two debates has advanced from 8 percent after the first debate to, as noted, 15 percent after the second. Those results underscore what's at stake in the candidate's last face-off tonight.

ABC News/Washington Post poll tracking since July 2012

CHALLENGES - While Romney shows momentum on some underlying attributes, he also still faces some fundamental challenges. Obama is benefitting from slightly improving economic attitudes; as many likely voters now say the economy is improving as say it's worsening, 37 percent vs. 36 percent, numerically positive for the first time since spring in comparable data.

Most strikingly, a majority continues to think Romney, if elected, would favor the wealthy rather than the middle class, by 54-33 percent. Obama, by contrast, consistently has been seen by an overwhelming majority, now 66-15 percent, as having done more to favor the middle class than the wealthy.

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Overcoming this perception may be Romney's single biggest challenge ahead; one complication in his addressing it is Obama's advantage in two other areas: Better understanding the economic problems of average Americans, on which the president leads Romney by 7 points; and honesty and trustworthiness, on which Obama's up by 9.

ISSUES and APPROVAL - Obama has an unusual advantage on another issue, again likely reflecting skepticism about Romney's economic priorities: In trust to handle taxes, typically a better issue for Republican candidates, Obama leads by 11 percentage points, 53-42 percent - the president's biggest lead on taxes all season.

Obama also is competitive with Romney in trust to handle the deficit, (49-45 percent, Romney-Obama); that's tightened from a wide Romney advantage in the spring and summer, perhaps reflecting some impact from Obama's continued criticisms of Romney's budget numbers. Obama, moreover, leads by 12 points on handling Medicare and by 13 points in trust to handle women's issues. Women prefer Obama on women's issues by a wide 18 points; men, by 7.

On trust to handle the economy - the election's top issue and Obama's greatest vulnerability - it's another virtual dead heat, 48-46 percent, Romney-Obama.

Still, Obama's job approval rating overall is 50 percent among likely voters, a point short of a majority. In historical terms, that can be adequate to win re-election (George W. Bush and, possibly, Harry S. Truman), but certainly not comfortably so.

While there have been shifts under the surface, it's notable how little overall preferences have changed in this contest: Obama's support among likely voters has been between 47 and 49 percent steadily since just before the conventions; Romney's, 46 to 49 percent. And likely voter definitions with different turnout estimates produce essentially identical horse race results.

STATES and GROUPS - As well as close overall, the contest stands at 51-47 percent, Romney-Obama, in the nine battleground states designated by the ABC News Political Unit - well within the margin of sampling error, and not significantly different from the mid-month 51-46 percent, Obama-Romney, in these same states. But regardless of sampling error, the bigger number now is Romney's, another indication of the competitiveness he's showing.

Obama has a little pushback on another metric: The share of his supporters who describe themselves as "very enthusiastic" has advanced to 64 percent, his highest of the season, and matching his level at this time in 2008 (but below his peak that year). Romney's strong enthusiasm, at 58 percent, is numerically off its peak at mid-month, after the first debate.

Among groups, again perhaps reflecting the second debate, this poll finds a shift in Obama's direction among college-educated white women. They go for Obama over Romney by 55-42 percent now, vs. a preference for Romney by almost an identical margin, 56-42 percent, in mid-October. Other slight shifts mitigate the overall impact - Romney's gained among white men, especially among those who lack a college degree - but it explains the wider gender gap.

Romney leads by 15 points among whites overall, while Obama comes back with a vast 78-19 percent advantage among nonwhites. There's a hardening at the ideological poles, with Obama and Romney at their highest support of the campaign among liberals and "very" conservatives, respectively (88 percent of liberals for Obama, 89 percent of very conservatives for Romney). The fight's among moderates, now +16 points for Obama, and somewhat conservatives, +37 for Romney.

There's also extreme polarization among Democrats and Republicans, with a scant 3-point difference between the candidates among independents, 49 percent for Romney, 46 percent for Obama. A slight 5-point turnout advantage for Democrats makes the race essentially tied - and, if nothing breaks open, makes turnout the key to the 2012 race. Turnout's especially important since a third of likely voters say they plan to vote early - including 5 percent who already have.

METHODOLOGY - This ABC News/Washington Post poll was conducted by telephone Oct. 18-21, 2012, among a random national sample of 1,376 likely voters, including landline and cell-phone-only respondents. Results have a margin of sampling error of 3 points, including design effect. The survey was produced for ABC News by Langer Research Associates of New York, N.Y., with sampling, data collection and tabulation by Abt-SRBI of New York, N.Y.

Partisan divisions in this survey, Democrats-Republicans-independents, are 34-29-33 percent among likely voters. Partisan divisions in the 2008 exit poll were 39-32-29 percent. "Battleground states" as designated by the ABC News Political Unit are Colorado, Florida, Iowa, Nevada, New Hampshire, North Carolina, Ohio, Virginia and Wisconsin.