In recent months, most of the Republican efforts to limit reproductive rights have been in state legislatures, as evidenced by recent fights in Texas, North Carolina, Ohio, and Wisconsin, among others.

But federal efforts on Capitol Hill haven’t faded, either. One notable Republican senator intends to take the lead.

Sen. Marco Rubio said unequivocally Wednesday that he hopes to be the lead sponsor of a bill banning abortions after 20 weeks. “If someone else would like to do it instead of me, I’m more than happy to consider it. But I’d like to be the lead sponsor,” the Florida Republican said. “I feel very strongly about this issue. And I’d like to be the lead sponsor on it if we can find language that we can unify people behind.”

If this sounds familiar, there’s a good reason – Rubio first expressed an interest in this three weeks ago, though there’s been little movement since. These new comments suggest the Florida Republican intends to make this a top priority.

There’s no shortage of relevant angles here. For example, Rubio, a long-time culture warrior and proponent of social conservatism, desperately wants to make the right like him again after his work on comprehensive immigration reform. Because the right places a high priority of abortion restrictions like these, it’s likely the senator sees this as a way to get back into their good graces as he moves closer towards a national campaign.

There’s also the larger effect on the Republican Party’s “rebranding” initiative. In recent years, as the GOP has become more extreme on issues like these, the party has exacerbated the existing gender gap thanks to the “war on women.” Instead of learning the right lessons, the U.S. House approved a 20-week ban championed by Rep. Trent Franks (R-Ariz.) last month, and even though it has no realistic chance of success, Rubio now hopes to follow suit in the U.S. Senate.

And finally, there’s the inherent policy problem of 20-week bans themselves.

To circle back to an item from a few weeks ago, Andrew Rosenthal had a good piece on the subject recently.

The way the Catholic Association mentions “late-term” abortions, you might think the only women who had them were lazy and callous, just waiting around until the last second for no good reason. But as Cecile Richards, the head of Planned Parenthood, told me in an email, nearly 99 percent of abortions occur before 21 weeks; abortions later on often involve rare, severe fetal abnormalities and real threats to a woman’s health. In many cases, women are facing the need to terminate a desired pregnancy, not an unwanted one. Ms. Richards cited the case of a woman in Nebraska, Danielle Deaver, whose water broke at 22 weeks, depriving her baby of most of the amniotic fluid. “Her doctor told her that the fetus could not develop or survive,” Ms. Richards said. “Despite this, she was forced to live through 10 excruciating days waiting to give birth, because her doctors feared prosecution under her state’s 20-week abortion ban.”

It’s exactly why medical associations consider proposals like Rubio’s so dangerous.