WASHINGTON — Within hours of each other, two federal appeals courts handed down separate decisions that affirmed sharp new limits on abortion and birth control. One on Oct. 31 forced abortion clinics across Texas to close. The other, on Nov. 1, compared contraception to “a grave moral wrong” and sided with businesses that refused to provide it in health care coverage.

“These are the kinds of decisions we are going to have to live with,” a blunt Senator Harry Reid, the Democratic majority leader, warned his caucus later as it weighed whether to make historic changes to Senate rules. Those changes would break a Republican filibuster of President Obama’s nominees and end the minority party’s ability to block a president’s choices to executive branch posts and federal courts except the Supreme Court.

The moment represented a turning point in what had been, until then, a cautious approach by Democrats to push back against Republicans who were preventing the White House from appointing liberal judges. All the more glaring, Democrats believed, was that they had allowed confirmation of the conservative judges now ruling in the abortion cases. Republicans were blocking any more appointments to the court of appeals in Washington, which issued the contraception decision.

Faced with the possibility that they might never be able to seat judges that they hoped would act as a counterweight to more conservative appointees confirmed when George W. Bush was president, all but three of the 55 members of the Senate Democratic caucus sided with Mr. Reid. The decision represented a recognition by Democrats that they had to risk a backlash in the Senate to head off what they saw as a far greater long-term threat to their priorities in the form of a judiciary tilted to the right.