We've also been able to track down the lyrics from the kids' song in the video:
Mm Mm Mm Barack Hussein Obama
He said that all must lend a hand
To make this country strong again

Mm Mm Mm Barack Hussein Obama
He said we must be fair today
Equal work means equal pay

Mm Mm Mm Barack Hussein Obama
He said we must take a stand
To make sure everyone gets a chance

Mm Mm Mm Barack Hussein Obama
He said red, yellow, black or white
All are equal in his sight

Mm Mm Mm Barack Hussein Obama
Some of these lyrics might seem awfully familiar.  Some of these lyrics have been borrowed from a traditional children's song called "Jesus Loves the Little Children," in which kids sing:
Jesus loves the little children
All the children of the world
Red, yellow, black, brown or white
They are precious in his sight
Jesus loves the little children of the world
This song is followed by another Carney-Nunes original, put to the tune of Battle Hymn of the Republic:
Hello, Mr. President we honor you today!
For all your great accomplishments, we all do say "hooray!"

Hooray, Mr. President! You're number one!
The first black American to lead this great nation!

Hooray, Mr. President we honor your great plans
To make this country's economy number one again!

Hooray Mr. President, we're really proud of you!
And we stand for all Americans under the great Red, White, and Blue!

So continue ---- Mr. President we know you'll do the trick
So here's a hearty hip-hooray ----