Davis and Ramsey expressed those beliefs during talks at a Hawkins County Republican Party Lincoln Day dinner held at the American Legion.
"If it's Fred Thompson versus (U.S. Sen.) Hillary Clinton, jump in and hang on," Ramsey, R-Blountville, told Hawkins County Republicans.
Retired U.S. Rep. William L. "Bill" Jenkins, the dinner's emcee, got the GOP crowd applauding early when he talked about the "Draft Fred" effort.
"We ought to call Fred collect and tell him what we are doing," Jenkins, R-Rogersville, joked.
"I have encouraged Fred to run," Davis, Jenkins' successor and a Johnson City Republican, said of the "Law and Order" television actor during his remarks. "I have signed on to his team. I think Fred is going to run. I think he would win the nomination and be president. He's got that common sense. ... Fred has got that conservative voting record. Fred is somebody we can be proud of just like Ronald Reagan."
Of the other GOP presidential hopefuls, Ramsey said U.S. Sen. John McCain isn't catching on with Republicans. New York City Mayor Rudy Giuliani's views on social issues won't sell in the South, Ramsey added.
Concerning former Massachusetts Gov. Mitt Romney, Ramsey said: "Massachusetts and conservative don't go into the same sentence."
While introducing Davis at the dinner, Jenkins recognized him for being critical of House Speaker Nancy Pelosi.
"Whatever criticism that old gal comes in contact with, she deserves it. ... She thinks she has taken on the role of the president, secretary of state and secretary of defense," Jenkins said of Pelosi, a Democrat.
"Hopefully we'll make her a member of Congress in just a few months," Davis said of Pelosi. "I really don't think the Democrats won last time (in the November 2006 elections). I think the Republicans lost last time. What we've got to do is get back to those fundamental Republican principles. If we do that, we can earn back our majority. This is a center right country. People want us to get back and do the things that are important."
Davis said if people have listened to Senate Majority Leader Harry Reid over the last few weeks, America has lost the war in Iraq.
"If we've lost this war like the Democrat leadership in Washington is trying to portray, that means someone has won," Davis said. "And who are we fighting? We are fighting the extremists. We're fighting terrorists. I hope and pray the day never comes that people in East Tennessee believe that we're going to let the terrorists win this war. ... It's too personal for us to give up."
Davis voted against the Iraq War spending bill that called for a timetable for withdrawal - legislation expected to be vetoed by President Bush.
"I see the veto happening early next week and I think we will have the votes to sustain President Bush's veto and I hope the majority party understands they will not get enough votes in Washington right now to turn our back on the troops," Davis told Hawkins County Republicans. "They will have to supply the funds needed to win this war. They have the power to cut off the purse strings. If they really think America is a failure, why don't they just stop the war now? We don't need this cut-and-run strategy. I think people voted for change in the last election. I'm just not sure they are getting the change they asked for."