Sen. Kay Bailey Hutchison (R-Texas) will announce Wednesday that she will serve out the remainder of her term, according to sources.

Hutchison's announcement is scheduled for this morning at 11 a.m. Eastern, and she'll be joined by fellow Texas Sen. (and National Republican Senatorial Committee Chairman) John CornynJohn CornynMcConnell: Senate could vote on 3 Trump nominees Friday Senate seeks deal on Trump nominees Overnight Healthcare: Takeaways from Price's hearing | Trump scrambles GOP health plans MORE and Senate Minority Leader Mitch McConnellMitch McConnellMcConnell breaks with Trump on NATO McConnell: Senate could vote on 3 Trump nominees Friday Dems engage in friendly debate for DNC chair MORE (R-Ky.).

Republicans have been asking Hutchison to serve out her term since before she lost her primary challenge to Gov. Rick Perry in February.

By staying, she spares her party the headache of a wide-open special election in which multiple Republicans might have run against a Democrat or two.

And two prospective successors have dropped out of the race to replace her.

Dallas Mayor Tom Leppert opted not to run on Tuesday, and now state Sen. Florence Shapiro is announcing that she will drop out and refund the $1 million she has raised for the race to her donors.