Washington (CNN) -- As the nation celebrated the start of another term for President Barack Obama, Republican congressional leaders had a muted, bipartisan response to his second inaugural address.
"Today is a day for all of us in this country to come together," House Majority Leader Eric Cantor, R-Virginia, told CNN, when asked about the president's speech. "It really doesn't matter who you voted for, which side you're on," Cantor added. "Today is a day we can all come together."
Cantor said the president's speech addressed the issue of upward mobility, a topic of shared concern across party lines.
When asked about online reaction to the speech from Republicans who felt it was too aggressive and too liberal, Cantor again refused to engage in partisan terms.
"I think the president did a fine job certainly laying out what he would like to see happen as far as the future of the country," the second-highest ranking Republican leader in the House said.
"There are plenty of areas of disagreement but there are also some things that, fundamentally, we agree on -- and that is this country is one of opportunity," he continued.
Cantor added that there were partisan differences over "the way we get there to help everybody. ... Hopefully, we can bridge those differences."
Cantor's remarks echoed a sentiment shared by Senate Minority Leader Mitch McConnell in a written statement issued as Monday's ceremony at the Capitol was beginning to wrap up.
"Every four years on Inauguration Day, America shows the world that our major political parties can disagree with civility and mutual respect," McConnell wrote.
The Senate's top Republican said Obama's second term represented a "fresh start" for addressing big challenges facing the country, including the issues of federal spending and debt.
"Republicans are eager to work with the president on achieving this common goal and we firmly believe that divided government provides the perfect opportunity to do so. Together, there is much we can achieve."
Obama, near the end of his inaugural address on Monday, made what appeared to be an oblique reference to the partisan battles between himself, the GOP-controlled House and the Senate -- where Democrats have control but do not have a filibuster-proof majority.
"Being true to our founding documents does not require us to agree on every contour of life; it does not mean we will all define liberty in exactly the same way, or follow the same precise path to happiness," the president said to the nearly one million people gathered along the National Mall. "Progress does not compel us to settle centuries-long debates about the role of government for all time -- but it does require us to act in our time.
"For now decisions are upon us, and we cannot afford delay. We cannot mistake absolutism for principle, or substitute spectacle for politics, or treat name-calling as reasoned debate. We must act, knowing that our work will be imperfect. We must act, knowing that today's victories will be only partial, and that it will be up to those who stand here in four years, and forty years, and four hundred years hence to advance the timeless spirit once conferred to us in a spare Philadelphia hall."
Obama added that "the oath I have sworn before you today, like the one recited by others who serve in this Capitol, was an oath to God and country, not party or faction -- and we must faithfully execute that pledge during the duration of our service."
Asked about what occurred during Monday's lunch attended by the president and some members of Congress, Cantor said, "It's a very nice lunch. It is really a continuum of the spirit of the day where both sides come together. There's bipartisan representation at the tables. There's legislative branch, judicial branch, executive branch all sharing tables. And just nothing but good. Hopefully that kind of cooperative spirit can continue."
Cantor said part of the reason the luncheon ran long was because Obama "went to every table and shook every hand."
CNN's Wolf Blitzer asked Cantor how long the bipartisan spirit and goodwill of Inauguration Day will linger.
"We hope that this lasts," Cantor said, "and then that we can focus on solutions, bridging differences, setting aside differences and trying to focus on what we have in common as Americans."