This is probably allowed, unless Texas has a 1 day or 1 case rule (which is common but hardly universal), in which case the potential juror could only be held for one day.
A juror can be compelled to be a juror against his will in any case in which he is qualified to serve. Usually, the legal authority of a court to compel a person to serve as a juror is much broader than the usual process for obtaining a juror.
If lack of impartiality in a particular case for case specific reasons disqualifies a person from serving on a particular jury, that doesn't mean that the person is disqualified from serving on all juries.
The judge's outburst isn't wonderful as a matter of judicial decorum, but the outburst probably doesn't undermine the judge's authority to compel the potential juror to serve in some jury pool. Ideally, this would have been expressed more calmly, but the bottom line is that you have a legal duty to show up and serve if you are qualified and a judge has broad discretion to see that this duty is fulfilled. Lots of people who will ultimately be dismissed without serving in a particular case end up having to sit around while the process determines if they are qualified to serve in any case.
Also, the judge is within his rights to punish the potential juror if he determines that the potential juror is actually lying about his ability to be impartial in an effort to evade jury service rather than because he sincerely believes that he can't be fair, and judges have wide authority to determine the credibility and truthfulness of statements made to him in open court (i.e. if the trial judge finds that you are lying, this determination will almost always be honored by an appellate court considering the judge's actions).
If someone complained about the judge's conduct to a judicial ethics body in Texas, the judge would very likely receive a private reprimand or maybe if the ethics panel was particularly incensed, a public reprimand, but only because he lost his cool on the bench, not because he required the potential juror to stick around until another suitable case could be found.