[See update at bottom]
Clause 2. When vacancies happen in the representation of any State in the Senate, the executive authority of each State shall issue writs of election to fill such vacancies: Provided That the legislature of any State may empower the executive thereof to make temporary appointments until the people fill the vacancies by election as the legislature may direct.
- Seventeenth Amendment
Unlike South Dakota, Wyoming provides a safeguard for the possibility that the resignation/death of a senator will result in a key Senate seat being appointed by a governor of a different party. See here as to the death of a Republican senator who some time back took over Cheney's seat in the House.
And, the state law requirement that the governor choose a member of the same party of the senator being replaced seems perfectly legal pursuant to the Seventeenth Amendment, which gives the legislature an option to let the executive provide a temporary seat. IOW, a state need not do so, it can leave the seat vacant until a special election (which is not required when a House seat falls vacant ... and the governor's choice here would not stay on to the next official election, which could be up to nearly six years in the future potentially -- the appointment is a stopgap until the election can take place).
[Update: Click the TPM link above to have the law here explained, a link to the law itself provided. In the comments, the author of that piece does a good job rebutting the Daily Kos Diary argument that suggests the law is unconstitutional. Besides, it has a taint of undemocratic to it, don't it? BTW, to clarify, when I say "next official election," I mean for the seat in question. The person who died just was re-elected, so technically (I guess) the appointment could conceivably serve to 2013. But, the law here requires another election the next general election (the law applies to various positions), which in this case would be 2008. This seems fair.]
The power of the legislature to set up the election and supply the contours of the executive appointment power appears open-ended, only limited by other provisions of the Constitution. And, I think it a good idea to have the temporary fill-in -- chosen not by the people but by one person -- in some fashion loyal to the person being replaced. This usually happens anyway, sometimes even by using the person's spouse or child, but not always. Likewise, the danger and fear is always there.
And, though we are talking strong Republican state here, the governor is Democrat.
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Update: One of the Amar brothers strongly supports the other view, so much that his column is in effect a brief in support of the governor's sole authority, when s/he is given it, to appoint without the strings here. I am willing to accept that this might be the case though the one sided implication from text and a bit of history doesn't impress too much, surely not the reference to a concurrence in Bush v. Gore (which apparently, first time I heard of it, O'Connor and Kennedy implicitly likely agreed with) citing (dubiously, including per precedent) stronger language respecting legislative power over presidential elections. Besides that dubious "precedent," where are these other cases that supported the "principle" argued here?
Simply put, the language in Sec. 2 here doesn't compel the argument made, the "empower" language not as absolutist and complete per the text alone as the article suggests. And, as to giving the legislature too much power, the executive appointment (optional to begin with) is only "temporary." Likewise, after all it are the parties, not the legislatures that supply the three options for the governor to pick from. Honestly, I think the text a bit thin, if anything a 10th Amendment argument (favored by some these days too) can be made that Wyoming was in no way limited by the Seventeenth Amendment, the immediate question left open.
And, the governor after all has to disagree with the choices in the first place for there to be any real problem in practice. I don't really see this happening. Still, I really don't see why the legislature while "empowering" the governor to fill vacancies cannot set up general regulations that apply to state offices too. The fact three justices in Bush v. Gore dubiously suggested otherwise really is not a good argument, is it? This in for a penny, in for it all argument -- see some of the comments to original TPM piece -- is perilous in the Bush administration, and is pretty perilous overall really.
No sale.