Colorado and Minnesota hold their caucuses Tuesday, followed by Maine on Saturday.
Romney canceled plans to attend a rally in Minneapolis on Monday, leaving that to surrogates while he focuses on Colorado.
He says he's the only candidate who can beat Democratic President Barack Obama.
Gingrich said he hopes to make a comeback by the time Super Tuesday rolls around on March 6.
"We believe by the time Texas is over, we'll be very, very competitive in delegate count and I think that the key from my standpoint is to make this a big choice campaign," Gingrich said.
However, he said if he does not succeed, "I will support the Republican nominee because reelecting President Obama would be a disaster."
Ron Paul was campaigning in Minnesota on Sunday, still looking for his first win.
"I think we have reason to be optimistic about not only our future, but maybe we have optimism about Tuesday's election too," Paul said.
Rick Santorum, who trailed in Nevada voting, was also in Minnesota touring a plant in the town of Bemidji, where they make sweater vests - his trademark.
"I feel confident that we're going to do well here in Minnesota," he said. "We're going to do well in Missouri on Tuesday and I think we're also going to do well in Colorado. At least I hope to do well in Bemidji, anyway."
Romney and other Republicans have been giving President Obama no credit for gradual improvements in the economy, or last week's drop in unemployment to 8.3 percent.
A new ABC News-Washington Post poll says both of those factors have helped boost the president's job approval rating to 50 percent, the highest since last spring. Forty-six disapprove.
In a potential matchup with Romney, the president leads among registered voters, 51 to 45 percent.