Thirteen months after his sinking Republican primary campaign launched its “No Surrender” tour in Sioux City, U.S. Sen. John McCain spent part of Sunday in north-central Iowa, kicking off the last full week of the 2008 general election on a similar note.

Sen. John McCain speaks in Cedar Falls. (Captured from CNN.com video.)

Sen. John McCain speaks in Cedar Falls. (Captured from CNN.com video.)

Trailing in most battleground states and facing a steep climb to victory, McCain was repeatedly confronted with questions about whether he can still win the election during a live broadcast of NBC’s Meet the Press, moderated by Tom Brokaw from the studios of KWWL in Waterloo.

McCain said he disputes the polls showing U.S. Sen. Barack Obama, his Democratic opponent, with a double-digit lead nationally. “It all depends on the voter turnout model,” he said. “We are very competitive in many of the battleground states.”

Later, on the campus of the University of Northern Iowa in Cedar Falls, McCain addressed a crowd of about 2,000 — a far cry from the 10,000 his runningmate drew a day earlier in the larger city of Des Moines — repeating familiar criticism of his opponent’s economic policy. “Sen. Obama’s tax increases would put even more people out of work,” McCain said. “We’ve seen this before in other countries, and it doesn’t work.”

He also said he planned to support new energy production, including offshore oil drilling, wind, solar, and ethanol. “We’ll invest in all energy sources,” McCain said. He has previously said — in debates, interviews, and campaign speeches — that he would end “ethanol subsidies.”

The Arizona senator placed more emphasis on the notion that Democratic leaders in Congress would be unchecked in an Obama administration. When McCain mentioned U.S. Rep. Barney Frank, D-Mass., the crowd booed in agreement with their candidate.

Then, he shifted to the horse race. “Let me tell you about the state of the race today,” he said. “The pundits, as usual, have written us off.”

Obama “is measuring the drapes. He’s planned his first address to the nation for before the election,” McCain said, referring to the 30-minute national television advertisement that the Obama campaign has scheduled for Wednesday night on CBS, NBC, and FOX. “I prefer to let the voters weigh in before presuming the outcome.”

“I am an American, and I choose to fight,” McCain said, building to a crescendo as he finished his speech. “Don’t give up hope. Be strong. Have courage, and fight.”

Unless the dynamics of the presidential race change soon, McCain will likely find himself repeating those words often over the next nine days.