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When ABC News’ Jonathan Karl asked President Obama this week at a press conference if Obama had “the juice” to get his agenda through the Congress, the president bristled and argued he was still relevant.

The question, while blunt, in part reflected the reality of Obama’s second term. The president is unlikely to find much success passing bills through Congress, not because he lacks skills of persuasion or juice, but because Republicans remain adamantly opposed to much of Obama’s agenda and have the ability to block it.

Other than immigration reform, the legislative route to policy achievements may be closed for the president unless Democrats regain control of Congress in 2014.

But that doesn’t mean Obama can’t have huge influence over American government and culture. For example, Obama’s  public comments on gay rights, from his support of same-sex marriage to his embrace of NBA player Jason Collins this week, were very significant symbolic actions.

Having the office of the president speak on behalf gay rights is important in shifting the country in that direction, even if not attached to legislation. (To be sure, Obama also took action legislatively in 2010, signing a provision that ended the military’s ban on people serving who are openly gay.)

The roll-out of Obamacare

On health care, Obama also pushed through a major bill three years ago. Successfully implementing that provision is no idle matter, but critically important and another area in which Obama has broad power. His administration is carefully negotiating with states that have Republican legislatures or governors, trying to convince them to accept provisions of Obamacare, particularly an expansion of Medicaid.

They’ve already reached a deal with the State of Arkansas that will extend health insurance to more than 200,000 people there. The Medicaid provision, which does not formally start until next year, could extend health insurance to more than 15 million Americans nationally if Obama and his team can convince Republican-run states like Texas and Florida to adopt it.

The president, according to aides, is also determined to create a diverse team of advisers, in part because he feels that is the right thing to do, but also because he wants to build a deeper bench for the next Democratic president. So his selections of minorities and women for key posts in his government are another area he can affect without Congress.

The Obama strategy going forward

Obama is also looking to appoint diverse candidates to federal courts, which only requires the consent of  the Senate, which is controlled by the Democrats.

Obama’s advisers privately concede the big, historic pieces of legislation that defined the president’s first two years, such as the health care law and Wall Street reform, are unlikely in a second term. So they are also looking for small-bore issue where the president can start a task force or give a speech and have influence without needing votes from Republicans, particularly in terms of helping Americans struggling to find jobs or pay for college.

None of this will look as lofty as Obama’s first term agenda. But there is room for Obama to work around the opposition of congressional Republicans and have a final four years of significance.

Follow Perry Bacon Jr. on Twitter at @perrybaconjr