Will they or won’t they? That’s the question as the Supreme Court nears the end of its term this month, and court watchers eagerly await a ruling in a case challenging the constitutionality of the Public Company Accounting Oversight Board.

The high court is expected to hand down its ruling in that case and several other high-profile cases this Thursday or next Monday, or possibly later next week. But there isn’t much time left as the Supreme Court traditionally ends its term in June, and the confirmation hearings for court nominee Elena Kagan are due to begin next Monday. Kagan argued the government’s case on behalf of the PCAOB as solicitor general, which would make it awkward for the court to rule against her arguments on the week of her confirmation hearings

The PCAOB’s constitutionality has been challenged by the Free Enterprise Fund, a conservative advocacy group, along with the accounting firm of Beckstead & Watts. So far they have lost their lawsuits in lower courts against the PCAOB claiming that the method of selecting board members violates the appointments clause of the Constituion and the separation of powers doctrine because only the SEC, and not the President, can remove the board members, and only for cause.

If the Supreme Court does rule against the PCAOB, it’s not likely that the board is going to instantly dissolve and auditing firms will be running wild around the country the next day. But it does mean there would be some changes coming in the board’s structure and perhaps even its members. No matter how the court rules, it could mean the board would finally get a permanent chairman as the uncertainty over the board’s status amid the Supreme Court fight has kept it with only an acting chairman, Daniel Goelzer, in place for nearly a year.

Even France’s official stock market regulator, the Autorite des Marches Financiers, seems to be wary of the PCAOB, reiterating an earlier ruling this week that the board does not have the right to inspect auditing firms in France, according to Dow Jones Newswires. If the U.S. Supreme Court throws down the gauntlet at the PCAOB too, it would certainly not be a great week for the beleaguered board.