WASHINGTON — Just about everybody agrees that Washington is a gridlocked mess. So who is the man to fix it? After two years of brawling and brinkmanship between President Barack Obama and congressional Republicans, more voters trust Mitt Romney to break the stalemate, an Associated Press-GfK poll shows.

Romney’s message — a vote for Obama is a vote for more gridlock — may be resonating. Almost half of likely voters, 47 percent, think the Republican challenger would be better at ending the logjam, compared with 37 percent for Obama.

With the race charging into its final week, Romney is pushing that idea. He increasingly portrays himself as a get-things-done, work-with-everybody pragmatist, in hopes of convincing independent voters that he can overcome Washington’s bitter partisanship.

The AP-GfK poll shows the race in a virtual dead heat, with Romney at 47 percent to Obama’s 45 percent, a difference within the margin of sampling error.

At a rally Wednesday in Coral Gables, Fla., Romney recounted how he worked with the Democratic-led legislature as governor of Massachusetts, and insisted he would find common ground with Democrats in Washington too. “We can’t change course in America if we keep attacking each other. We’ve got to come together and get America on track again.”

Obama made his own show of bipartisanship Wednesday, touring superstorm Sandy devastation alongside Republican Gov. Chris Christie in New Jersey. A major Romney supporter, Christie has been praising Obama’s “outstanding” response to the natural disaster.

Obama counters the Washington gridlock question by predicting that Republican lawmakers focused on opposing his re-election will become more cooperative once he wins a second term and becomes ineligible to run again.

Referring to the top Republicans in Congress, Obama joked that he would “wash John Boehner’s car” or “walk Mitch McConnell’s dog” to help get a federal deficit-cutting deal.

Obama also argues that Romney is more conservative these days than when he was elected governor, and will find that his newer ideas don’t go down easily with Senate Democrats.

In the AP-GfK poll, about 1 out of 6 likely voters didn’t take a side on the gridlock issue, 6 percent weren’t sure who would do a better job at getting Washington moving, and 10 percent didn’t trust either man to break the impasse among congressional partisans.

“They all need to be taken by the ear by a grandma,” voter Margaret Delaney, 65, said in frustration.

She lives in Janesville, Wis., the hometown of Republican vice presidential nominee Paul Ryan, and she is leaning toward voting for the GOP ticket.

But when it comes to ending gridlock, Delaney thinks it may not matter whether Romney or Obama is president. “I’m not sure either of them can do it,” she said.