A different way to think about it is in terms of LBJ and Harry Byrd. One of Johnson’s first acts as president was to order his staff to abandon the Kennedy Administration’s fight with Senator Harry Byrd of Virginia over the size of the federal government. He told them to just abjectly surrender to Byrd and agree to arbitrary cuts. In exchange for agreeing to arbitrary budget cuts, Byrd was willing to agree to a tax cut bill that the administration’s economist (and many liberal members of congress) thought would boost the economy. Then with the tax cut bill passed, a filibuster of civil rights legislation was no longer also holding up the tax bill which was important to keeping the “pro” side together throughout an extended debate.
The right question about health care and stimulus, in other words, isn’t whether “focusing on jobs” would have had some magical impact on the Congress to induce them to pass a stimulus bill. The question is whether some concrete logroll was available in which some members of Congress would have been willing to back a stimulus bill in exchange for Obama abandoning universal health care.
Now to the best of my knowledge no offer even remotely resembling that was on the table. But by the same token, to the best of my knowledge nobody in the White House attempted to explore anything like that. If you look at the now-infamous Romer/Bernstein stimulus chart, one of the things that pops out at you is that the administration believed in 2009 that powerful equilibriating forces would push the economy back to full employment fairly rapidly even in the absence of any stimulus at all. The point of stimulative policies was to cushion the blow, but they expected full employment conditions to return by 2013 one way or another. Paul Krugman said at the time that this was too optimistic, but there’s every reason to believe the administration believed that was an accurat forecast. Operating within that framework, abandoning longstanding policy objectives in order to obtain extra stimulus would have been pretty ridiculous. So nobody on the Hill or in the White House explored the issue.