Sen. Scott Brown, in a tough race for re-election in heavily Democratic Massachusetts, said of Romney's comments: "That's not the way I view the world."
Still, with high-profile presidential debates and seven weeks of campaigning yet ahead, others said those concerns were overstated.
"I don't expect the negative headlines of this week will be what we're talking about a week from now," said Fergus Cullen, the former Republican state chairman in New Hampshire and a close ally of Romney. Like other Republicans, he said, "It's incumbent on the Romney campaign to make it (the election) about Obama's handling of the economy."
Top Republicans in Congress volunteered no reaction to Romney's remarks - just as they generally refrained from commenting a week ago when he issued a statement that inaccurately accused the Obama administration of giving comfort to demonstrators after they breached the U.S. Embassy in Cairo.
In the days since, Republicans have grumbled that Romney needed to sharpen his appeal to struggling middle class Americans by stating more clearly what he would do as president to help them. That effort began overnight with a new ad designed to appeal to female voters.
The controversies blazed as opinion polls showed Obama moving out to a narrow lead nationally and in some of the key battleground states in the two weeks since back-to-back national political conventions.
The sluggish economy and lingering high unemployment are by far the overriding issues of the election, and Romney's case for the presidency is based on his claim that his success as a businessman has left him the skills needed to create jobs in a nation where unemployment is 8.1 percent.
Obama and the Democrats have tried to counter by depicting the president's challenger as a multimillionaire who has some of his wealth invested in the Cayman Islands and elsewhere overseas, and is out of touch with the needs of middle class Americans.
In his original reaction to the video, posted by the left-leaning magazine Mother Jones, Romney told reporters Monday night that his fundraising remarks were "not elegantly stated." But he offered no apologies and did not answer directly when asked if he felt he had offended anyone.
He also called for the release of the entire video, rather than selected clips, and Mother Jones did so Tuesday afternoon.
By then, the magazine had already posted another excerpt in which Romney offered an unvarnished assessment of the chances for peace in the Middle East. "The Palestinians have no interest whatsoever in establishing peace," and "the pathway to peace is almost unthinkable to accomplish," he said.
"You hope for some degree of stability, but you recognize that this is going to remain an unsolved problem," he said, "and we kick the ball down the field and hope that ultimately, somehow, something will happen and resolve it."