Would this fix President Obama's IRS problem?

No. After abuses of the IRS under FDR, Kennedy, LBJ, and most notably Nixon (thanks Eisenhower and Truman for not abusing the IRS, but every other President in that era did) Congress finally insulated the organization from direct Presidential control. There were abuses of the IRS under Bush when they audited a left wing church, but there was never any connection proven that went back to the White House (it should have been investigated more closely). Similarly here, there is no evidence of any connection to the White House. If there is a connection, that would be a big deal. It should be investigated so we can know for sure, but so far, it appears to be internal to the IRS.

Getting someone fired from the IRS is, and should be, a difficult thing for the President to do. Holder is looking into criminal charges and the Inspector General and Congress are looking at further investigations. The IRS should simply fire the people involved on their own, but the President can't just order them to do it. His control over the organization is too attenuated for that.

EDIT: By the way, your letter slightly misstates the problem. It's not that groups were targeted based on their name, it's that the targeting was done based on buzz words that align with a political ideology. If they had used a more sophisticated mechanism (or at least a non-partisan one) to pick out applications that appeared to be for political groups seeking to abuse the 501(c)4 status, a practice that has become very common after Citizens United, there would be nothing wrong with that. But you can't target Tea Party groups and not Occupy groups. Nor can you target only those two. You've got to either use a very broad collection of buzz words or else use non-partisan ones like "for America".

We don't know yet where exactly this decision was made. It appears that the efforts to mitigate it were inappropriate, as the agency knew about the problem for a year and didn't immediately fire those involved. But at this point, we don't know that the intent was anything more than simply to save time in culling through these applications which have doubled since Citizens United. If it was partisan, that's probably criminal and Holder may prosecute. If it was just a dumb way to save time, obviously the people involved should be fired as should the supervisors who tried to fix the problem but keep it internal. We should investigate to see if this goes farther up the chain than that, but there is no reason at this point to think it does.

Lets face it the IRS has been corrupt for awhile.

The right calls a flat tire an Obama problem while protecting crooks

No. Nothing would make the Obama-bashers happy. And, btw, do you really think these guys were stupid enough to put this in memos?

I think the lady who runs the IRS should be fire purely for one reason, if not for this scandal. In an interview I heard she said "I'm not very good at math". HOW can you run the IRS and NOT be good at math. WTF.