Sanchez has twice run statewide, losing the gubernatorial race to Democrat Bill Richardson in 2002 before capturing the state's No. 2 job in November.
"People in the state are looking for new ideas," he said. "They're not looking to return to policies of the past, and decisions and leaders that kind of got us into this mess in the first place."
Sanchez said the support of Tea Party activists won't be the deciding factor in the primary race. "I don't necessarily need to be the Tea Party candidate," he said, noting he shares their values of "lower taxes, less government."
"If those are the values that I share with the members of the Tea Party, then so be it," he said.
The Republican brushed off the suggestion that his run for Senate could anger voters who elected him to his current job less than six months ago.
"The opportunity to serve is really the issue at hand right now," he said. "It's about serving and the opportunity to serve the people of New Mexico and this county.
"Those opportunities for an open United States Senate seat don't come but once in a lifetime."
Sanchez said he would decide on a run "relatively soon."
"We believe that a decision will be coming very quickly," he said, noting that "tax day," when returns are due to the IRS, was coming up in April. "We think that sometime here in the near future, in the spring, we'll be making a final decision as far as what our intentions are."
He continued: "Based on the support that we've been receiving from supporters in New Mexico and throughout the rest of the country, we're very encouraged with the amount of early support and encouragement."
Sanchez said he hadn't met with the National Republican Senatorial Committee, but planned to do so when he returned to Washington next week.
"I haven't had any conversations with them yet, but I know that people throughout New Mexico and, actually, across the country have shown tremendous interest in my potential run for the U.S. Senate," he said.