All together now?

 A few days after the 2008 election, a USA Today/Gallup poll asked "In dealing with the problems facing the country, do you think Barack Obama will make a sincere effort to work with the Republicans in Congress to find solutions that are acceptable to both parties?" and parallel questions about whether the Republicans would make a sincere effort to work with the Democrats and Obama and whether the Democrats would make a sincere effort to work with the Republicans.  In March and September 2009 they asked about whether the various parties had made a sincere effort to work with each other, and in February 2010 they asked about working together on health care reform.  They also asked the forward-looking questions after the 2010, 2012, and 2016 elections.  The figure shows the percent who said that Obama, the Democrats, the Republicans, or Trump would (or had) worked with the other party:

Obama consistently ran ahead of both the Democrats and Republicans in Congress, and the Democrats were generally somewhat ahead of the Republicans, but they all rose and fell together.   In principle, you might expect that they would move in opposite directions at least some of the time:  that people would see one side as being obstructionist and give the other side credit for trying, but that didn't happen with any of these surveys.  Rather, the public seemed to blame both sides about equally when there was disagreement (if anything, Obama's ratings might have fallen more than the Congressional parties).  

I think this data helps to explain why Republicans turned against the Senate immigration deal.  If it had passed, Biden would have gotten some of the credit from the public, and most Republicans are unwilling to do anything that will make Biden more popular (several of them said as much).  A few years ago, I suggested that a strategy of uniform opposition had driven down Obama's popularity.   Republicans have continued with that under Biden.  Of course, there has been some important bipartisan legislation, like the American Rescue Plan Act, but they were mostly early in his term and my impression is that the Republicans have tried to avoid publicizing them.  It used to be that when popular legislation was passed on a bipartisan basis, both parties would talk about it and try to claim some of the credit.  But more recently, people seem to have realized that elections are more about the President than about Congress, so for an opposition party, denying credit to the President is more important than claiming credit for yourself.  And blocking potentially popular legislation might make your side less popular, but it will probably make the other side less popular as well.

A few other observations:

1.  The numbers expecting the parties to make a sincere effort to work with each other were higher than I expected. 
2.  Just after the 2016 election, 58% expected Trump to make an effort to work with the Democrats, which was somewhat ahead of the number who expected the Republicans in Congress to work with the Democrats.  That might be because in 2016, many people saw Trump as a "dealmaker" rather than a traditional conservative, or it may be that there is a tendency to have hopes for a new president.  
3.  It's not possible to be sure, but it seems that the questions that asked about the future produced more positive responses than those that asked about the past.
4.  Following from the previous points, it's unfortunate that this question hasn't been asked since 2016--I would like to see how expectations have changed.

[Data from the Roper Center for Public Opinion Research]