Sen. Lindsey GrahamLindsey GrahamSenate rejects ObamaCare repeal, replacement amendment Trump turns up heat on AG Sessions over recusal OPINION | McConnell attempt to butcher ObamaCare is political malpractice MORE (R-S.C.) said that Republicans "made some pretty poor choices" in choosing their Senate candidates this fall.

Graham, in a Senate floor speech on Saturday, made an aside comment underscoring the frustration the GOP faced after some Tea Party-aligned nominees fell short in their campaigns.

"The House had a dramatic election. We picked up seats in the Senate," Graham said, video of which is posted by C-SPAN. "Some of us thought, maybe we could pick up two or three more, but we made some pretty poor choices when it came to candidates."

The South Carolina Republican made the comment as an aside to remarks about the consequences facing lawmakers who vote to allow an increase in taxes. Senate Democrats fell short of the necessary votes in a rare Saturday vote that would have allowed taxes go up on top earners.

Still, Republicans bargaining position in those votes and in legislative fights next year might have been strengthened had the party's nominees performed better in Senate races.

Many of the Tea Party favorites who won GOP primaries went onto disappointing finishes in the general election, some in races where Republicans needed to win if they were to have any hope of reclaiming a Senate majority. Those losing candidates included Christine O'Donnell in Delaware, Ken Buck in Colorado, and particularly Sharron Angle in Nevada, where Republicans had hoped to knock off Senate Majority Leader Harry ReidHarry ReidConservative Senate candidate calls on GOP to end filibuster Ex-Reid aide: McConnell's 'original sin' was casting ObamaCare as 'partisan, socialist takeover' GOP faces growing demographic nightmare in West MORE (D-Nev.).

Graham is seen as a possible incumbent who might face a primary from a Tea Party type when he's up for reelection in South Carolina in 2014.