President Obama, with golfer Zach Johnson, left, and House Speaker John A. Boehner (R-Ohio), speaks at a ceremony honoring the 2013 President's Cup U.S. team during a ceremony in the East Room of the White House in June. (Jacquelyn Martin/Associated Press)

President Obama and his signature health-care law are as unpopular as ever, and Republicans appear increasingly likely to ascend in the 2014 midterm elections. There's even a surprising amount of support for impeaching Obama.

And yet, when it comes to House Republicans' lawsuit against Obama's use of executive orders regarding the Affordable Care Act, support is languishing.

A CBS News poll last week showed that Americans oppose the lawsuit, which focuses on Obama having unilaterally delayed the employer mandate portion of the legislation, 54 percent to 37 percent.

A couple of weeks ago, another poll -- from CNN and Opinion Research International -- showed a similar split, with Americans opposing the lawsuit 57 percent to 41 percent.

These surveys are somewhat surprising, given a few things:

1) The same CNN poll showed 45 percent of Americans think Obama has "gone too far" in expanding the power of the executive branch. In other words, some people who think he has gone too far don't think it warrants a lawsuit.

And it might even be a bigger split than the CNN poll suggests. CNN asked a three-pronged question, allowing people to say Obama has gone too far, hasn't gone far enough or has been "about right." Generally, people are drawn toward the middle-ground response -- in this case, "about right" -- if they don't feel strongly. Three in 10 people chose that option.

And sure enough, a Fox News poll from two weeks ago asked people a yes-or-no question about whether Obama had gone too far when he changed the health-care law using an executive order. Americans answered in the affirmative, 58 percent to 37 percent.

So, to recap, as many as six in 10 people think Obama exceeded his authority in this case, according to one poll, but just four in 10 support the lawsuit, according to two other surveys.

2) As we've written before, a lawsuit would seem to be a more moderate/supportable alternative to impeachment. But polling has shown that only slightly more people support the lawsuit than support impeachment -- which, it bears mentioning, entails the potential removal from office of the president.

CNN showed an eight-point difference in support (33 percent on impeachment vs. 41 percent on the lawsuit). But the Fox poll showed support for impeachment as high as 36 percent -- just one point below the CBS poll's 37 percent support for the lawsuit.

Comparing similar questions on different surveys doesn't yield an apples-to-apples comparison, but it does show how there's not a whole lot of daylight between Americans' views of the lawsuit and impeachment.

3) Americans have previously been supportive of such congressional probes.

When the House GOP began investigating what happened in Benghazi, Libya, a poll showed that Americans approved of it 51 percent to 42 percent. Similarly, three-fourths of Americans supported appointing a special prosecutor to look into the IRS scandal.

So it's not like whatever Republicans do when it comes to oversight of the executive branch, such things will automatically be dismissed by moderates as petty partisan politics. The American people are quite willing to support looking into and checking the executive branch when it's warranted.

In this case, though -- despite the unpopularity of the law and of Obama -- the American people do not think it's warranted.