Yes they do, but their grip over hearts and minds isn't what it used to be. As they lose their grip, they get more and more extreme.
In the 60s, there wasn't any alternative to the Big 3 nets and the AP-WaPo-LAT-NYT alliance, which singlehandedly swung public opinion and, with the help of feckless leadership from LBJ, lost the War in Vietnam.
When Roe v Wade was decided in 1973, there was no meaningful alternative to their lockstep feminist agenda.
We had to get to 13% inflation and 20% interest rates before a true conservative could go over the heads of the alliance and get elected.
In 1993, they thought they could roll a national healthcare plan over us with no opposition. WRONG-Rush Limbaugh and nationalized talk radio stopped it.
In 1998, they thought they could laugh impeachment off the stage. WRONG-The slick one got impeached, though not convicted, as the nascent Internet and tidal wave of Talk Radio got the truth out.
In 2003, the pro-death alliance is desperately trying to use the traditional media to advance their agenda in the Terri Schiavo case. You know it's serious when the ACLU jumps in-AGAINST HER. Years ago, I believe she would have died with relatively little fanfare. Not this time.