The die is cast in the GOP race for president. You can't undo the attacks by Romney on Gingrich and Santorum or Santorum's withering blasts at Romney. And because of that, the rest of the public sees the jostling in a much different light.

A new Battleground poll by Politico/George Washington University reveals the harm being done to the party's chances in November:

"We've not been talking about which would do a better job of running against Obama. We've been talking about who is the most or who is the least conservative," said Republican pollster Ed Goeas of The Tarrance Group, who helped conduct the bipartisan poll. "That is a problem for Republicans."

Get full poll results and analysis.

A third of Americans believe the country is on the right track - disconcertingly low for a president eight months before an election. Yet that figure is twice the number who believed it in November.

Romney is bloodied after nine contests, five of which he has lost. Only 33 percent of independents view him favorably, compared with 51 percent who see him in an unfavorable light. In a head-to-head match-up against Obama among independents, Romney now trails 49 percent to 27 percent.

Among Republican voters nationally, Santorum narrowly edges out Romney, 36 percent to 34 percent. Newt Gingrich is a distant third with 13 percent, and Ron Paul gets only 7 percent.

Santorum's slight advantage is striking because Romney holds significant leads over the former Pennsylvania senator among likely primary voters on which of the four remaining candidates would best handle jobs (14 percentage points), the economy (19) and balancing the budget (21). Of five areas tested, Santorum leads Romney only on social issues.

Those net unfavorables are appalling. Romney's showing with indies, abysmal. The "electability" factor hardly matters if these numbers get much worse. It may get to the point that the GOP will nominate a candidate who can keep Obama's margin of victory down so that GOP senate prospects have a chance.

Obama is eminently beatable. But as long as the GOP candidates beat each other up rather than focus on Obama's failures, the voters will decide accordingly.