File: Sen. Ted Cruz (R-Texas) (Joel Page/Reuters)

Sen. Ted Cruz (R-Tex.), a conservative torchbearer and potential presidential contender, turned his attention to local D.C. politics Wednesday by introducing a measure in Congress to upend one new city law regarding discrimination over reproductive health decisions and another to keep religiously affiliated colleges in the nation’s capital from having to fund gay and lesbian student groups.

The measures, known as disapproval resolutions, could in theory halt local laws passed last year by the D.C. Council and signed by the city’s mayor. But to do so, Cruz’s measures would require support of both chambers of Congress and the signature of President Obama.

Although rarely successful at stopping D.C. laws, the resolutions are often more effective politically, giving members of Congress legislative records to build bona fides with constituent groups that feel strongly about the District’s often liberal stances on social issues.

On the two issues at hand, there are more than a few with strong feelings.

Last month, more than a dozen prominent conservative groups and Catholic institutions asked Capitol Hill leaders to overturn the two D.C. laws, calling them “unprecedented assaults upon our organizations.”

The laws would restrict the ability of private groups to discriminate based on religious beliefs. One, the Reproductive Health Non-Discrimination Amendment Act of 2014, would prevent employers from taking action against workers based on their decision to use birth control or seek an abortion. The other, the Human Rights Amendment Act of 2014, repeals a longstanding, congressionally imposed measure exempting religiously affiliated educational institutions from the city’s gay nondiscrimination law.

As is the case for all D.C. laws, the two are now under a mandatory 30-day review period before Congress. Without congressional action, they could take effect as early as next month. That happened last month with the city’s marijuana-legalization law, when, despite threats from House Republicans, no lawmaker introduced a measure to stop it. Some Republicans feared a vote on marijuana legalization could expose a rift between conservative and libertarian wings of the party.

Asked about the measures Wednesday while walking through the U.S. Capitol, Cruz referred questions to his office, which did not immediately respond to a phone call and e-mail seeking comment.

Freshman Sen. James Lankford (R-Okla.), who co-introduced the measures, issued a statement Wednesday saying “what the D.C. Council has done is a major threat to the fundamental right to religious freedom for D.C. residents and organizations, and a brazen display of intolerance.”

As evidence that Congress would be within its rights to disapprove the D.C. measures, Lankford pointed to a Supreme Court decision last year that family-owned businesses do not have to offer their employees contraceptive coverage under the Affordable Care Act if doing so conflicts with owners’ religious beliefs.

“Last summer’s Supreme Court decision affirmed the right to live and work in accordance with your convictions. In America, a person can choose a lifestyle of any faith or no faith at all — that’s religious freedom,” Lankford said. “Washington, D.C., residents and organizations shouldn’t be discriminated from enjoying those same rights.”

In a statement, Kimberly Perry, head of D.C. Vote, an organization that lobbies for voting representation for the District in Congress, criticized the effort as counter to Republicans’ belief in greater states’ rights.

“Senators Cruz and Lankford’s move to disapprove a local District law is absurd and hypocritical,” Perry said. “They are now guilty of the same federal overreach they often criticize in others.”

Perry called on “every other member of Congress to step up and see this for exactly what it is — un-American and un-democratic.”

The letter last month opposing the proposed D.C. laws was signed by leaders of Heritage Action for America, the Family Research Council and the National Organization for Marriage, as well as representatives from the Catholic University of America,the Archdiocese of Washington and the U.S. Conference of Catholic Bishops.

Conservative commentators have sharply criticized both bills, particularly the human rights measure, which would repeal the 1989 “Armstrong Amendment” passed in response to a lawsuit filed under the D.C. Human Rights Act to compel Georgetown University to recognize a gay student group. Georgetown, notably, was not among the signers of the new letter.

The D.C. Council this month attempted to head off some of the brewing controversy over the bills. The council passed an emergency amendment to the reproductive health law to clarify that employers could not be forced to provide insurance coverage for contraception and abortions that they oppose on religious grounds.

The council initially had said the amendment was unnecessary because that was made clear last year by the Supreme Court, but the fix to the bill was pushed by D.C. Mayor Muriel E. Bowser (D).

Referring to the Cruz measure to upend the abortion-related law, Bowser spokesman Michael Czin said that because District residents have no vote in Congress, the mayor intends to work with allies in Congress and the president “to stave off this intrusion into private discussions between doctors and their patients.”

“From fixing our broken immigration system to investing in our nation’s ailing infrastructure, there are numerous issues that deserve the attention of members of Congress. The District of Columbia’s legislative process should not be one of them,” a statement from the mayor said.

Religious groups were more pleased Wednesday. “These bills are serious violations of religious freedoms,” said Casey Mattox, senior counsel with the Alliance Defending Freedom, a conservative Christian legal group. “We are pleased members of Congress are taking them seriously.”