Wait for Dunn to open a door and start the next big part of the fight. The first area is split between 2 rooms. There are Russians to the left and right, so just get behind something solid and use your shotgun to take them out. Clear out both rooms and feel free to use a few grenades. Go straight through to make it to the press conference area. Start clearing the press room as best as you can. Focus your gunfire and try to stay close to the rangers.

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Your goal is to get over to the press stands and metal monitors in your way. Kill the 2 Russians that charge forward to the left side. Once that's done, you can basically just settle in at this safezone. Lay down steady gunfire to thin out the Russians at the other end of the room. Once you've got a path cleared out, you can move over to the left side and go out. Take cover behind one of the garden walls. There should be about 3 guys near your position, if the rangers didn't kill them already. 3 more should rappel down the White House to get on the roof opposite of you. Take them out as they descend for a few easy kills. 2 more should come out at the end of this little path. Kill them. You should then be able to charge down to the end and flank the remaining Russians.
We're close to the time limit, but it shouldn't be any problem if we just follow Foley and hustle a bit. Get up the ramp and kill the Russians at the top. Then spin around and quickly gun down this final position. There should be about 5 guys spread through the area. Stay back by the ramp and snipe any enemies that you can, then gun them down with a simple charge. Sprinting up and stabbing a guy is also surprisingly effective. Get up the steps in back to meet up with the other team on the roof. Follow the marked soldier out to wave your green flares and call off Hammer Down.