Hillary Clinton does have a right to remain in the running as long as she wants.
And she does have a case that the voters in Michigan and Florida should not be faulted or punished because of the actions of elected leaders who gambled on moving those primaries up. The intent was to get some of the national media attention (not to mention campaign spending) that was focused on the early primary states. Of course the elected leaders lost on that account. Especially in Michigan-- Obama took his name off the ballot, and all the state got out of it was a somewhat competitive GOP primary that only saw two candidates campaign much and gave Mitt Romney his biggest win of the primary season-- a win which was not all that big, in fact. Florida at least can make the case that John McCain's win, coming just after his South Carolina win and just before Super Tuesday may have played a decisive role in the Republican race. One can only imagine what kind of thoughts must have crossed the minds of those who moved the primaries up, complaining that otherwise they wouldn't have had a voice, watching all the attention and campaign money that was lavished on Pennsylvania for six full weeks leading up to that state's April 22 primary.
At the same time, Barack Obama has a case that he can make that the results from last January don't represent what would have happened if he and Senator Clinton had campaigned in the two states. Obviously being named on the Michigan ballot would make a difference, but beyond that in both primaries a lot of independents, having been told that the Democratic primary would not matter at all, cast their votes in the Republican primaries. Obama has consistently outpolled Clinton among independents (and until Rush Limbaugh started urging conservatives to vote for Clinton, he also outpolled her among crossover Republicans) so it is virtually certain that had the primaries been competitive Obama would have done quite a bit better than he did.
But I did some math, and even if she makes her case for Florida and Michigan, she still is extremely unlikely to catch him.
According to the BBC tally if the results were counted fully and as voted, they are:
Hypothetical Florida result (elected delegates): Clinton 113, Obama 72, John Edwards 13
Hypothetical Michigan result (elected delegates): Clinton 80, Uncommitted 55
If we take the numbers currently reflected on the Real Clear Politics scoreboard we see that as of right now, Obama leads Clinton 1959-1778 in total delegates (counting both pledged delegates and announced superdelegates.) There are also 55 delegates remaining to be selected from Puerto Rico, 15 from South Dakota and 16 from Montana.
If we add all 193 Clinton delegates from Florida and Michigan to her total and the 72 Florida delegates to Obama's total, we still would have Obama leading 2031-1971, a lead of sixty delegates. She would then need to replicate her West Virginia margin, 70-30 in all three of the remaining contests (unlikely given Obama's appeal in the plains states) just to get to a tie. And that's giving Clinton EVERYTHING, including counting all the rest of the uncommitted and Edwards delegates as uncommitted (not for Obama.) In reality, that won't happen-- it is no secret that people who voted 'uncommitted' in Michigan were voting primarily for Obama (and most of the rest for Edwards), and since Edwards' endorsement of Obama, nearly all of his convention delegates have unsurprisingly followed his recommendation and moved over to Obama.