No, it's not illegal.

The US Supreme Court has never been asked to rule on the legality of state-sanctioned Christmas trees, but in Allegheny County v. Greater Pittsburgh ACLU, it did rule that a crèche forming part of a Christmas display which happened to also include a large Christmas tree violated the Establishment Clause (and conversely that the inclusion of a menorah in the same display did not).

In that opinion, the court did have this to say about trees:

The Christmas tree, unlike the menorah, is not itself a religious symbol. Although Christmas trees once carried religious connotations, today they typify the secular celebration of Christmas.¹

Indeed, the court concluded in that case that the inclusion of the tree in the display was a mitigating factor, reducing the likelihood that the menorah could be seen as an overt endorsement of religion.

If they were illegal, presumably some enterprising member of Congress would have tried to impeach the President by now...

No, it's not illegal.

The US Supreme Court has never been asked to rule on the legality of state-sanctioned christmas trees, but in Allegheny County v. Greater Pittsburgh ACLU, it did rule that a crèche forming part of a christmas display which happened to also include a large christmas tree violated the Establishment Clause (and conversely that the inclusion of a menorah in the same display did not).

In that opinion, the court did have this to say about trees:

The Christmas tree, unlike the menorah, is not itself a religious symbol. Although Christmas trees once carried religious connotations, today they typify the secular celebration of Christmas.¹

Indeed, the court concluded in that case that the inclusion of the tree in the display was a mitigating factor, reducing the likelihood that the menorah could be seen as an overt endorsement of religion.

If they were illegal, presumably some enterprising member of Congress would have tried to impeach the President by now  ...

No, it's not illegal.

The US Supreme Court has never been asked to rule on the legality of state-sanctioned christmas trees, but in Allegheny County v. Greater Pittsburgh ACLU, it did rule that a crèche forming part of a christmas display which happened to also include a large christmas tree violated the Establishment Clause (and conversely that the inclusion of a menorah in the same display did not).

In that opinion, the court did have this to say about trees:

The Christmas tree, unlike the menorah, is not itself a religious symbol. Although Christmas trees once carried religious connotations, today they typify the secular celebration of Christmas.¹

Indeed, the the court concluded in that case that the inclusion of the tree in the display was a mitigating factor, reducing the likelihood that the menorah could be seen as an overt endorsement of religion.

If they were illegal, presumably some enterprising member of Congress would have tried to impeach the President by now  ...

No, it's not illegal.

The US Supreme Court has never been asked to rule on the legality of state-sanctioned Christmas trees, but in Allegheny County v. Greater Pittsburgh ACLU, it did rule that a crèche forming part of a Christmas display which happened to also include a large Christmas tree violated the Establishment Clause (and conversely that the inclusion of a menorah in the same display did not).

In that opinion, the court did have this to say about trees:

The Christmas tree, unlike the menorah, is not itself a religious symbol. Although Christmas trees once carried religious connotations, today they typify the secular celebration of Christmas.¹

Indeed, the court concluded in that case that the inclusion of the tree in the display was a mitigating factor, reducing the likelihood that the menorah could be seen as an overt endorsement of religion.

If they were illegal, presumably some enterprising member of Congress would have tried to impeach the President by now...