If President Barack Obama has soured on pointless haggling with congressional Republicans, the feeling is mutual.

So after Tuesday evening’s post-State of the Union platitudes about working together have been dispensed with, expect House and Senate Republicans to go their own way, ignoring Obama and his demands as much as possible.

Republicans still vow to engage with Obama, and fight him, on issues that require collaboration, the budget and the debt ceiling included. But much as Obama regretted the Washington-centric debates of his first term and took to the road early and often since winning re-election, House Republicans plan to shift from perpetual combat with the president in favor of a broad legislation agenda that focuses on voters and sets the table for 2014 — and even 2016.

“We can’t just sit here for two years and deal with the things the president throws at us,” a House Republican leadership aide said Monday. “We’re going to take our agenda outside of Washington.”

In the Senate, the Republicans’ minority status could force them to play defense in an effort to respond to an agenda that is controlled by the Democrats and usually an extension of policies being pushed by the White House. But in the House, where Republicans run the floor, the party plans to shift gears, spearheading a series of bills designed less to land on the president’s desk than to communicate to Americans what the GOP stands for.

Given the outcome of the 2012 elections and the increasing importance of Hispanic and younger voters, it also is likely no accident that Speaker John A. Boehner of Ohio and Senate Minority Leader Mitch McConnell of Kentucky selected the 41-year-old Rubio, an ethnic Cuban, to deliver this particular Republican rebuttal to the State of the Union address. Rubio is not just a rising GOP star and potential 2016 presidential contender, but a key Republican leader on immigration changes.

“Marco Rubio is the right guy to talk to Hispanics about work ethic and economic growth as a counter to deficit spending,” said a Republican lobbyist with relationships on Capitol Hill. The implicit suggestion of many Republican operatives is that Rubio is an important GOP messenger to spotlight in the aftermath of the party nominating a 2012 presidential candidate who garnered a mere 27 percent of the Hispanic vote.

For Rubio, the task offers risks as well as rewards — a fact that is probably not lost on the politically savvy senator. Delivering the GOP rebuttal further elevates his profile and affords him an opportunity to establish a relationship with voters of all political stripes. But following the president on his annual stage, absent the energy and cheering of the House chamber, has humbled rising politicians of both parties. A poorly reviewed rebuttal has hobbled the presidential prospects of some.

In the House, much of the Republicans’ voter-focused legislative agenda could sprout from the seeds planted by Majority Leader Eric Cantor of Virginia in a speech he delivered last week. The theme of the address was “making life work,” and it foreshadowed the intent of House Republican leaders to move their conference away from constant confrontation with Obama and toward a direct conversation with voters on how GOP policies can improve their lives.

Cantor said Sunday on NBC’s “Meet the Press” that bills on the topics he discussed in the speech, including education, economic growth, health care and immigration, would be rolled out in the coming weeks and months. And, in fact, sources said Monday that the Virginia congressman vetted the speech with Boehner, GOP committee chairmen and other leaders before delivery to secure support for moving legislation through the House.

Republicans are still bracing for brutal fights over federal spending, enacting a fiscal 2014 budget and raising the debt ceiling, and many are relishing the debate.

But just as Obama has moved to broaden his agenda beyond fiscal issues and turned to executive orders to implement change opposed by the GOP, House Republican leaders hope to take control of the political debate by eschewing fights with the president and pursuing a more diverse policy course than that which guided the first two years of their new majority and focusing attention on what they would do if they ran Washington.

“We have to find the will to drive an agenda again,” a House Republican aide said. “It must be common sense to gain traction. and it must not ignore the everyday problems that Americans are facing or we will look out of touch.”