WASHINGTON — Can Rick Perry rebound from a troubled September? How will Herman Cain endure his first test as a heavily-scrutinized candidate? And will Mitt Romney, debating in a state where he's a strong favorite, stay on his cool, steady course?

Those are the key questions as the Republican presidential candidates meet again Tuesday in Hanover, New Hampshire, for their first debate in 19 days. The topic is supposed to be economic issues. The debate begins at 8 p.m. EDT and will be televised nationally by Bloomberg TV.

The encounter, about three months before the first-in-the-nation New Hampshire primary, is likely to matter in small but important ways.

"People don't know any of these people well," said Peter Brown, assistant director of the Quinnipiac University Polling Institute, which conducts national surveys. Debates are a chance for voters to get familiar and comfortable with candidates.

New Hampshire voters are already familiar with Romney, who was governor of neighboring Massachusetts, has a home in Wolfeboro, N.H., and finished second in the state's 2008 Republican presidential primary with 32 percent.

Romney remains the unquestioned New Hampshire favorite. In the WMUR Granite State poll conducted Sept. 26 to Oct. 6, he was the choice of 37 percent of likely Republican voters. Cain, the business executive who vaulted to prominence last month by winning the Florida GOP straw poll, was next, at 12 percent.

Trailing were Texas Rep. Ron Paul at 9 percent; former New York City Mayor Rudolph Giuliani, who is not expected to enter the race, at 8 percent; former Utah Gov. Jon Huntsman, 8 percent, and former Texas Gov. Perry, 4 percent.

But the poll also illustrated why these debates matter: 86 percent of likely Republican voters said they are extremely or very interested in the race, and 68 percent said they were still trying to decide on a candidate.

"Most people don't make up their minds till the end," said Andrew Smith, director of the University of New Hampshire Survey Center.

So the questions become: Who can cement the image of themselves as a serious contender? Who can best push the economy out of its doldrums? And who can be the chief conservative alternative to the more center-right Romney?

"We're looking for a non-establishment candidate to emerge," said Jane Aitken, an organizer of the New Hampshire Tea Party Coalition. "The tea party is hoping that the 70 percent who don't like Mitt Romney will coalesce behind a non-establishment candidate who's conservative."

Perry, who entered the race in mid-August, was seen as hurting himself in his three September debate performances, and has continued to generate controversy.

Earlier this month, the Washington Post reported seven people said that a racial slur — "Niggerhead" — has been legible for years on a large rock at the entrance to a West Texas Perry family hunting camp. Perry said the family had it painted over in the early 1980s, and strongly condemned the term recently as "very offensive."

As that controversy simmered, Dallas pastor Robert Jeffress backed Perry during a Washington, D.C., conservative conference Friday. Jeffress later referred to the Mormon religion as a "cult." Romney and former Utah Gov. Jon Huntsman, also debating Tuesday, are Mormons. Perry's campaign said the governor does not believe Mormonism is a cult.