The CultureWarNotes.com headlines make the implication:
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First, on March 26 came this piece by Austin Ruse, president of Catholic Family & Human Rights Institute, in The Catholic Thing

A reliable source tells me that someone representing the Obama administration is about to put pressure on the papal nuncio to the United States to get Archbishop Raymond Burke to be quiet. The Obama complaint is that Archbishop Burke, who is now head of the Apostolic Signatura in Rome, has supported another bishop in his chastisement of KS Gov. Kathleen Sebelius for her support of abortion….
Sebelius… has been nominated to head the massive US Dept. of Health and Human Services….
And now there is word that someone who is well known among Republicans, and who has served in previous Republican administrations, is reaching out on behalf of the Obama administration to get the Holy See to quiet Burke, or at least to make it clear he speaks not for the Church, but only for himself….

That was preceded March 25 by this in CNSNews.com piece:

In an interview in Rome with Catholic activist Randall Terry, Archbishop Raymond Burke said that Catholics who voted for President Barack Obama engaged in “a form of cooperation” with evil because of Obama’s pro-abortion policies.

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If a Catholic knew that abortion was gravely sinful and that Obama wanted to make abortion more available and voted for him, that Catholic “cooperated” and bears a responsibility for the consequences, said Burke.
Burke is an American and head of the papal courts at the Vatican. On Wednesday, Randall Terry screened a DVD of his interview with Burke at the National Press Club in Washington, DC….

Terry’s press conference was followed the next day, March 26, the same day as the Ruse piece, by a terse chastisement from Burke, according to US News & World Report:

Randall Terry… is… in hot water with a highly placed Roman Catholic bishop. Yesterday, Terry held a press conference in Washington to promote his campaign to pressure more US Catholic bishops to deny Communion to politicians who support abortion rights….
Terry played a videotaped interview that he recently conducted in Rome with Archbishop Raymond Burke, a top Vatican official. But Burke has quickly issued a statement disavowing Terry’s campaign:
Recently, Mr. Randall Terry and some of his associates visited me in Rome and asked to videotape [still from video below left] an interview with me to share with pro-life workers for the purpose of their encouragement. The interview was conducted on March 2, 2009.

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Sadly, Mr. Terry has used the videotape for another purpose which I find most objectionable.
First, Mr. Terry issued a media advisory which gave the impression that I would be physically present at the press conference during which he played the videotape, when, in fact, I was in Rome.
Second, I was never informed that the videotape would become part of a press conference.
Third, I gave the interview as a Bishop from the United States to encourage those engaged in the respect life apostolate, not as the Prefect of the Supreme Tribunal of the Apostolic Signatura.
Fourth, I was never informed that the videotape would be used as part of a campaign of severe criticism of certain fellow bishops regarding the application of Canon 915 of the Code of Canon Law.
If I had known what the true purpose of the interview was, I would never have agreed to participate in it.
I am deeply sorry for the confusion and hurt which the wrong use of the videotape has caused to anyone, particularly, to my brother bishops.

Has Obama so quickly succeeded in getting Rome to shut Archbishop Burke up? Burke did clarify in his statement he was speaking on his own, not on behalf of the Vatican – as Ruse said was at the very least requested.
Of course, what do I know? But I’ve tracked Archbishop Burke since he was such a strong pro-life stalwart in WI (where I’ve even visited the Shrine of Our Lady of Guadalupe, which he founded) and then as he remained strong in St. Louis before being assigned to Rome.
I don’t know anything about Vatican politics, but I just don’t see Archbishop Burke caving to pro-abortion pressure.
However, if I were Randall Terry, I wouldn’t have wanted to get out of bed this morning. I would die if my church leaders thought I had betrayed their trust and then publicly chastised me.
For those interested, here are Parts I and Part II of Terry’s interview with Archbishop Burke, which I think Terry should have immediately removed from YouTube after reading Burke’s statement. His not doing so to me is a shocking display of ursurpment of his Church’s authority, which in my nondenom Christian Church (my faith) world is a HUGE breach.
[HT: Facebook friend Steve Kellmeyer]