WASHINGTON (AP) — Mitt Romney struggled to steady his presidential campaign on Friday, buffeted by an outbreak of sniping among frustrated Republicans, fresh evidence of a slide in battleground state polls and President Barack Obama’s accusation that he was writing off ‘‘half the country’’ in pursuit of the White House.

Republican running mate Paul Ryan drew boos at an AARP convention in New Orleans when he said Romney would repeal Obama’s health care law, which closed a gap in coverage for seniors’ prescription drugs. The Wisconsin congressman accused the administration of weakening Medicare and flinching from tough measures needed to stabilize Social Security’s finances, adding that the president has ‘‘put his own job security over your retirement security.’’

Obama rebutted Ryan’s charges point by point in a video appearance to the same audience. He said the Republican prescription for Medicare would mean ‘‘billions in new profits for insurance companies’’ and replacing guaranteed benefits with a voucher that would bring higher out of pocket costs for seniors.

Romney campaigned in Nevada as aides released a 2011 federal income tax return showing he and his wife, Ann, paid $1.94 million in federal taxes last year on income of $13.7 million. Their effective tax rate was 14.1 per cent, lower than many families pay because most of the couple’s earnings come from investments.

The campaign also released a letter from Romney’s doctor saying the 65-year-old former Massachusetts governor is healthy and physically up to the demands of the presidency.

Romney continued to point to Obama’s recent remark that he had learned, after nearly four years as president, that he couldn’t change Washington from the inside. Although Obama went on to cite public involvement as a necessity for change, the Republican campaign framed the remark as an admission of failure.

‘‘Over history there have been people that have changed Washington from the inside,’’ Romney said in Las Vegas. ‘‘And they've done it effectively by showing leadership from the top. ... This president has not done that.’’

But there seemed no letup in the bad political news for Romney, hit by a barrage of it since he was seen on videotape saying that his job as a candidate is not to worry about the 47 percent of Americans whom he said pay no income taxes and see themselves as victims.

In an interview taped for broadcast Sunday on CBS’ ‘‘60 Minutes,’’ Romney said of his campaign: ‘‘It doesn’t need a turnaround. We've got a campaign which is tied with an incumbent president to the United States.’’

Obama, for sure, was eager to keep the controversy alive. Campaigning in Woodbridge, Va., he defended himself against Romney’s jabs at his own statement that change is impossible from the inside in Washington. ‘‘It can’t happen if you write off half the nation before you even took office,’’ he said.

He also drew laughter and applause from his audience when he mocked his rival. ‘‘He stood up at a rally, proudly declared, ‘I'll get the job done from the inside.’ What kind of inside job is he talking about? Is it the job of rubberstamping the top-down, you're-on-your-own agenda of this Republican Congress? Because if it is, we don’t want it.’’

According to Wall Street Journal/NBC News/Marist Poll surveys, the president has opened leads among likely voters of eight percentage points in Iowa, with 6 electoral votes, and margins of five percentage points each in Colorado (9 electoral votes) and Wisconsin (10.)

Earlier surveys published this week pointed to leads for Obama in both Virginia, with 13 electoral votes, and Ohio, with 18.

National polls have been far closer, including an AP-GfK survey this week that had it a statistical tie among likely voters. They have also suggested progress for Obama in terms of his handling of the economy, the No. 1 issue in the race.

Despite Romney’s difficulties, recent soundings on employment have not been encouraging for the president’s re-election. Newly released figures show joblessness ticked up in five swing states in August, fell in two and was unchanged in two others.

Romney’s allies also point to a series of presidential debates beginning Oct. 3 as a chance to shake up the race.