My thoughts on this issue:
Holding the media responsible for public perceptions is a convenient rationale for political leaders from both parties to explain why they have not met goals, among other things. However, almost always it is only a small part of the story. Instead, one needs to look at the interpersonal dealings: how the political leaders and their rivals interacted, the degree to which they focused on ideological goals at the expense of common ground, etc.
It is early to write any kind of historical narrative on the Obama Administration, but the early contours are emerging:
1. Fiscal stimulus: He devoted a lot of energy to get this legislation passed. The nation was facing what amounted to an economic emergency so to speak. Maintaining TARP (a last act of leadership by the Bush Administration) and adopting a stimulus program were key aspects of what amounted to an economic stabilization and turnaround strategy. The stimulus, though, was viewed through an ideological lens outside the economics profession, which mainly regards it positively though having fallen short of what was required given the post-stimulus data that emerged. The recession was deeper than had been known at the time. From a political standpoint, political capital was expended due to the ideological gap. Historians probably will judge him as demonstrating leadership on this issue.
2. Affordable Care Act (ACA): Health care reform is viewed through an ideological prism. That access was lacking (as shown in the high incidence of uninsured persons), medical costs were rising persistently faster than inflation (complex reasons e.g., early deployment of technology when cost efficiencies are poor), and outcomes on key benchmarks (also complex) were lower than numerous developed countries (so-called "peers") indicated a need for reform. How to reform the nation's health system saw the two parties as far apart as one could possibly get. Aside from small aspects of the ACA e.g., creating an access mechanism for people with preexisting conditions, there was almost no common ground between the two parties. The ACA was a legacy goal for President Obama and he succeeded in having it enacted, it survived constitutional review, and it was a focus of a disastrous shutdown strategy launched by Senator Ted Cruz et al. Its rollout was also very bumpy. Following on the heels of #1, the ACA hardened the ideological divide and it was probably too much for the GOP to bear, limiting opportunities for future pragmatic collaboration. Historians will likely judge him as demonstrating leadership on this matter, but making a fateful choice that could only dramatically impair his ability to work with GOP going forward. Choices have consequences.
3. The rise of the Tea Party movement further hardened the ideological divide. That the Tea Party movement's momentum has stalled and its influence is slowly decaying is not going to lead to a dramatically different opportunity for collaboration following the 2014 elections. There might be some modest changes, mainly in avoiding the near self-inflicted debt ceiling crises and unnecessary government shutdown that dominated the most recent years, but not much more.
4. Fiscal differences: Both sides essentially "blamed" the other for the failure to reach a grand budget accord. The reality is that acknowledging sincere differences precluded a deal at the time would have preserved latitude for future efforts at collaboration, particularly if events narrowed some of the areas of difference. One can expect blame from certain members of Congress who are in almost continual campaign mode. The President could and should have been more diplomatic. He wasn't. His blunt public comments amplified the perceptions stemming from the ideological divide.
5. The President anecdotally has spent less time nurturing and sustaining relationships with key Congressional leaders than some of his predecessors have. President Reagan and Speaker O'Neill, for example, spent a lot of time talking. So did President Clinton and Speaker Gingrich starting during the government shutdowns. Reagan and O'Neill built a personal relationship that transcended their deep political differences. Clinton and Gingrich built a working relationship after those shutdowns that allowed them to get things done for most of the rest of President Clinton's second term. One cannot same the same for President Obama. IMO, he could and should have had a much better relationship with many of the GOP leaders, excepting the Tea Party members who are much more wed on ideology than practical problem solving. He didn't. Hence, those Congressional leaders had less incentive to be pragmatic and accommodating than might otherwise have been the case.
In sum, the President had to deal with a structural environment that was trending more and more ideological, in large part due to factors beyond his control. That limited some of his opportunities. He also made choices that built the policy road ahead: fiscal stimulus (necessary, IMO, and not a "deal breaker") and the ACA (a key goal, but not necessary in the same sense the stimulus was, but a legacy goal that he was determined to realize). He also did not make the kind of effort needed to build strong personal relationships with Congressional leaders (Democratic and Republican), and this further limited his opportunities.
In short, I believe he could have done more with the proverbial cards that were dealt. Some of the reduced results are on account of factors beyond his control, but others are on account of factors that were controllable, but were shaped by personal choices and actions e.g., lack of time building personal relationships. Personal relationships are no guarantee of governing success, but they do make things a little easier and, even when sincere differences exist, can avoid the creation of damaging perceptions that amplify those very real differences. Indeed, better relationships with the Congressional leaders might have led to their tamping down the politically-motivated efforts expended on such matters as the Benghazi terrorist attack, etc., that have further poisoned the GOP-Obama relationship.