The loss of voting rights in the General Assembly is the only tangible repercussion which would be imposed. Note that the loss of voting rights is automatic - it doesn't rely on a resolution passing the General Assembly or Security Council to take effect.
The question of the loss of UNSC voting rights in particular was raised in 1998, when the US was significantly in arrears. Although negotiations between the UN and the US eventually led to a significant amount of the debt being paid, in exchange for a reduction of the assessment ceiling rate (the maximum proportion of the UN's budget which a single country can be required to pay) from 25% to 22%, there was a long period of uncertainty as to whether the US would pass the two-year arrears cap and lose their GA vote.
In a press conference in September, Fred Eckhard, Spokesman for the Secretary-General, was asked whether the United States would lose its right to vote in the Security Council when it lost the right to vote in the Assembly for non-payment of arrears:
No, Mr. Eckhard answered, article 19 would apply only to the General
Assembly. "And I might mention that it is not an action that Member
States would take to remove the right to vote from the United States.
It is an automatic result of a calculation made at the end of the year
of the arrears, and all Member States who are more than two years
behind by the calculation automatically lose their vote." Action would
have to be taken by the Assembly to grant an exception, Mr. Eckhard
added. "That is not to suggest it would happen, but that is possible."
As far as non-tangible repercussions, then Secretary General Kofi Annan gave a speech a few weeks later, where he echoed the words of Supreme Court Justice Hugo Black:
But the news for United Nations funding is grim indeed. It appears
that the United States will squeak by, paying just enough to avoid
losing its vote in the General Assembly, which happens to nations who
fall two years behind in their contributions. I wish to stress that
this is something that happens automatically, under Article 19 of the
United Nations Charter; it is not something that other Member States
do to others.
So while the United States will avoid this fate for this year, on the
larger question -- its legal commitment and moral obligation to the
United Nations and the 184 other Member States -- the United States
will have failed.
Great nations keep their word. They do not inflict wounds on their own
prestige or undermine their claim to leadership at crucial moments in
world affairs. I can only hope that when Congress reconvenes, we can
get this issue behind us. The United States needs an effective United
Nations; the United Nations needs an engaged United States.
At least in Annan's view, then, the failure of the United States to meet its budget obligations would harm the authority of not just the United States, but also the United Nations.