WASHINGTON — In one Senate office building, some of the leading lights of the Democratic Party gathered Wednesday to embrace what was once a proposal only of the far left: a huge expansion of Medicare, large enough to open the popular, government-run health program to all Americans.

In another Senate office building, a smaller but equally adamant group of Republican senators stood together to take one last stab at dismantling the Affordable Care Act. They proposed instead to send each state a lump sum of federal money, along with sweeping new discretion over how to use it.

Important elements in both parties are trying to move beyond President Barack Obama’s health care law, which has always been a complicated, politically difficult mix of government and private health insurance. But they are moving in radically different directions.

The proposals appeared to have only one thing in common: Neither is likely to be enacted any time soon.