What did Katniss mean when she says "trust me"?

Question

At the end of the first Hunger Games movie:

Katniss says "trust me" to Peeta when she proposes that they both commit suicide rather than fight.

What does she mean by this?

Does she believe they will be spared, or does she believe they will die and she is comforting him?

Answer 1

It seems that Katniss was thinking the former.

A couple of sentences before the one you quote, she thinks this:

If Peeta and I were both to die, or they thought we were . . .
^{-The Hunger Games, Chapter Twenty-Five.}
[emphasis added]

So she's hoping that the Capital or at least the Gamemakers don't let her go through with it. She surmises this:

Yes, they have to have a victor. Without a victor, the whole thing would blow up in the Gamemakers’ faces. They’d have failed the Capitol. Might possibly even be executed, slowly and painfully while the cameras broadcast it to every screen in the country.
^{-The Hunger Games, Chapter Twenty-Five.}

In a way also, Katniss confirms that she knew the likely outcome of the stalemate in Catching Fire:

“I have a problem, Miss Everdeen,” says President Snow. “A problem that began the moment you pulled out those poisonous berries in the arena.”
That was the moment when I guessed that if the Gamemakers had to choose between watching Peeta and me commit suicide—which would mean having no victor— and letting us both live, they would take the latter.
^{-The Hunger Games - Part Two: Catching Fire, Chapter One.}
[emphasis added]