Since Social Security withholding rates went up in the 1980's, the SS Trust Fund has collected far more money than it needed to pay out current benefits. That remains true. All money the Government collects from SS withholding goes immediately into the Federal general fund. Simultaneously, bonds are issued to the SS Trust Fund for that amount which they can then cash to pay current benefits as needed. The excess accrues interest until it is needed for benefits. Under the current system, it is expected that these bonds will have to be all redeemed in 20-30 years. After that, the trust fund will not get enough money from workers to pay full benefits. That is what has to be fixed for long-term solvency.
It is legally possible, but not required that the President hold up SS payments. He can do nothing, and it will still be legal for Treasury to pay SS benefits. If he chooses, he can prevent the Treasury from honoring the bonds and stop SS payments, perhaps to use it as a bargaining chip in current negotiations. I believe he will not do this, because there is no amount of "spin" that will make anyone but the Democrats responsible. If he does it, the Democrats will not win another national election, maybe for decades, and they will not win many Congressional elections, either.
Buck