If this was a crash project with no expenses spared, it is possible in theory.
SpaceX currently is the only rocket company building boosters on an assembly line, so their hardware can be pressed into service. Three Falcon 9 boosters strapped together make a Falcon9 Heavy, which can launch heavy payloads into orbit, including ones with powerful trans stages to get into interplanetary orbits.
Dragon capsules can hold up to seven astronauts apiece, although for trips like this, you probably want to only hold 4, both to minimize launch weight and make the on board supplies stretch out. Each Dragon will be mated in orbit with a Bigelow inflatable jabhab module, which provides space for the astronauts and supplies in flight. With some clever handwaving, it may be possible to gently aerobrake the Bigelow modules and have them eventually come to a stop floating in the Venesian atmosphere like giant balloons.
The problem is "now what?"
Unlike the colonists who escaped to the Moon, Mars or the asteroid belt, the colonists on Venus are trapped. Any resources they need will have to be "mined" from the atmosphere, which is Carbon Dioxide with a smattering of water vapour and sulphuric acid. Mineral resources are hidden miles below under a hellish 90 atmospheres of pressure, temperatures similar to the interior of a self cleaning oven and under the gravity field of a planet similar in size to Earth.
In contrast, the other colonists have access to a wide range of resources, including water, and are on bodies which only require a small amount of energy to enter orbit and escape to interplanetary space. Venesians will be like people trapped aboard a balloon; they can actually see the ground below and all the resources, but have no means of getting there to replenish the piknick baskets they brought with them (and current technology will not allow them to bring anything to Venus that they can use or adapt for surface mining, much less boosting it back into orbit).
So Venus may be a target for exploitation in the centuries to come (skimming the atmosphere will provide lots of CO2 to use as feedstock for making artificial diamonds and grapheme for industry), but this will require a mature infrastructure to be developed in space, and plenty of R&D as well.
Head to Mars, young man.