That depends on what the "crisis" is.
It would have to be a crisis ginned up unrelated to the NBC issue. If a court declared Obama ineligible, his orders would not be followed. I don't think Obama has broken a sweat over the NBC issue yet and he appears to have a deeply layered defense which is batting 1000 so far. He was very vulnerable before inauguration, but was protected because he was viewed as too precious to fail or vet by the media and all members of congress.
Now as president, only one federal judge, Judge Carter, has even opined that Obama is vulnerable to a quo warranto. We don't know whether any other federal court or SCOTUS will agree and this is dragging on towards Obama's renomination without resolution. Even if subject to quo warranto, we can't be certain that Obama will be judged non-NBC by the current SCOTUS. They refused to cert the issue when D'Onofrio gave them a chance (though it is not clear what the refusal was based on).
Some folks seem to forget that the 1948 BNA, which Obama has invited us to apply to himself, requires a legitimate non-bigamous marriage to pass UK citizenship to BHO II and 1902 Kenya Marriage Act seems to preclude legitimacy for the Dunham-Obama marriage. Illegitimacy as an exclusion to creating dual citizenship was accepted and known at the time that Chester Arthur's legitimacy was challenged.
Danae recently discussed and quoted 19th century investigator Collins as follows:
"A lawyer and scholar by the name of George D. Collins Esq. wrote an article regarding citizenship during Arthurs term, that had the President seen it, would have concerned him. Are Persons born Within the United States Ipso Facto Citizens thereof? was published in the American Law Review in Sept. /Oct. 1884."
"Collins concludes:
"'Birth, therefore, does not ipso facto confer citizenship, and it is essential in order that a person be a native or natural born citizen of the United States, that his father be at the time of the birth of such person a citizen thereof, or in the case he be illegitimate, that his mother be a citizen thereof at the time of such birth.' Collins"
http://www.examiner.com/examiner/x-7715-Portland-Civil-Rights-Examiner~y2009m12d14-Americas-Two-Unconstitutional-Presidents
Danae and others like D'Onofrio have focused on the part of Collins' quote regarding whether or not the father is a citizen, but in this passage Collins declares explicitly that if a baby is illegitimate, it can still be a natural born citizen if the mother is a citizen, as Obama's mom was.
On the "not born on US soil" issue, Obama has a COLB from HI which meets the federal rules of evidence as being "self-authenticating". This is an extremely high bar to refute, and at this point only a quo warranto hearing that would require Obama to produce "best evidence" would result in disclosure of the "vital records" underlying the COLB.
Following HI vital record disclosure a subsequent investigation of anything suspicious (whatever Obama has been hiding so desperately) would have to open up the possibility of a non-USA birth to threaten Obama. Then such evidence of a foreign birth would have to be authenticated for example by notoriously corrupt Kenyan authorities. If the vital records only show a home birth, but no smoking gun for a non-HI birth (evidence of foreign birth that meets federal rules of evidence), then ineligibility due to foreign birth will be a dead end. Hey, it is a long hard road, but well worth the effort!
Does he?
I know of no one not firmly in the 0bama camp or with even the slightest clue how to determine authenticity of a birth certificate who even claims to have actually seen the alleged document.
OTOH millions of people have seen an image of the alleged document on the internet.
It's on the internet, it must be true...