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: Mueller 'ought to wrap it up' Senate rejects effort to boost Congress's national security oversight Graham jokes about Corker: GOP would have to be organized to be a cult MORE and Senate Minority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellCongress had a good couple of weeks — now let's keep it going McCarthy: 'The Mueller investigation has got to stop' McConnell: Mueller 'ought to wrap it up' 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.