That belief is not based in law or the Constitution. The former doesn't speak at all to this issue, and the latter is maddeningly vague on this specific point.
The actual, legal realities are:
The problem is what to do if Obama is found to be ineligible. Becoming ineligible is simple enough -- the President is removed and the Vice-President takes over. I.e., President Biden, who would then nominate a new Vice-President, to be appointed with advice and consent of the Senate.
Of course, if Obama had been found to have been ineligible prior to Congress' ratification of the Electoral College vote, the matter would also have been simple (Constitutionally, though certainly not palatable to the Democrats), then no (valid) candidate would have achieved an Electoral College majority, and therefore the House of Representatives would have to select one of the top 5 (valid) people having received Electoral College Votes. But there was only one person who qualifies under that scenario: John McCain, who would be President with Joe Biden as his Vice-President.
The problem arises in that the Constitution makes no provision for when a sitting President becomes ineligible because it was shown that he never was eligible in the first place. In this case, it would likely be up to Congress to deal with the matter (as they are the judge of elections and nothing in the Constitution would restrain them, apart from the actual eligibility requirements). I would expect that they would do the most politically expedient thing: declare the office vacant, and then proceed as in the first scenario above with President Biden.
--The case alleges Congress failed to follow the Constitution, which "provides that Congress must fully qualify the candidate 'elected' by the Electoral College Electors."
“I would expect that they would do the most politically expedient thing: declare the office vacant, and then proceed as in the first scenario above with President Biden.”
You may well be right. But if Obama held the office illegally, shouldn’t that invalidate every Executive Order and even some bills he has signed since Jan. 20, 2009? Admittedly, Joe Biden could sign all these bills/orders himself, but in some cases, these bills would have been considered “pocket-vetoed” since Congress recessed during the 10-day period that the Constitution gives the president to sign a bill. That would appear to apply to health care reform reconciliation, since Congress plans to recess for Easter etc.
Both houses of Congress. Per the 25th Amendment.
I agree. As I see it, most of these lawsuits (though I admit to not wading through the pleadings in great detail) bite off way too much in that they ask the court to be the first fact-finder. A better strategy might be to plead the facts show that nowhere in the process is the constitutional eligibility standard adquately safeguarded. IOW, that these facts show that the process is not sufficient to keep someone who may be ineligible from being seated as president. The court would not actually have to find Obama ineligible.
Then the Congress would have to come up with a standard, a process, and a procedure for review and a remedy. However, it would help if the Court would tell us upfront explicitly what constitutes "natural born citizenship."
The standing issue, sorry to say, is one of those judicial doctrines that ends up being a simple way to expand or contract jurisdiction based on whether or not the Court wants to get involved. Of course the SCOTUS would not want to rule on a president's eligibility, especially a president as unpopular as Obama. If they could see their way to rule on the sufficiency of the legislative effort, if any, to safeguard the constitutional eligibility requirement, they'd be protecting the Constituion and still showing great deference to the legislature.