"The last man they thought wouldn't keep his word"

Writing on the health care bill, Elizabeth Drew illustrates GOP party discipline with a Mississippian example:

In mid-December 2009, Republicans were threatening to filibuster the defense appropriations bill for the acknowledged purpose of delaying consideration of the health care bill, which was to follow. (They were thus holding up pay and supplies for the troops fighting in Iraq and Afghanistan; if the Democrats did that, they would be charged by the Republicans with treason.)

The Democrats believed that they had a deal with Thad Cochran of Mississippi, the senior Republican on the Defense Appropriations Committee and widely admired as a courtly and honorable man, to adopt some amendments he wanted to the defense bill; in return he would provide the sixtieth vote to shut off the filibuster on defense appropriations. (One Democrat was holding out on this vote.) But then the Senate Republican leaders, in particular the dour whip John Kyl of Arizona, leaned heavily on Cochran, telling him that the Republicans had to stick together and make the Democrats come up with their own sixty votes. "It was kind of an agonizing ordeal for me," Cochran told me later.

In some instances, Republicans who might shun the leaders' demands are given indications that their future committee assignments might be affected; and they can be made to feel very lonely in conference meetings. Cochran's Democratic colleagues watched in amazement as the last man they thought wouldn't keep his word quietly raised his hand to cast his vote (he couldn't even say it) against shutting off the filibuster on the defense bill, and quickly left the Senate floor. If the Republican leadership is willing to treat Cochran--who is third in seniority among Senate Republicans and would be chairman of the Appropriations Committee if the Republicans were in the majority--in this way, it's not hard to imagine how more junior members are treated.

But it's not clear "in what way" Cochran was treated. What were they going to do to him? What could they have done? Why did Cochran think kowtowing to his masters was necessary? What "future assignments" or lonely conference meetings matter to Cochran at this point in his career?