I disagree. What's wrong with that? A political party is an artificial construct - a group of people who share some common interests, generally most interests, but disagree on others. If the Republican Party is fitfully falling apart, as it has seemed to be since at least 2010, then there can be no greater stabilizing influence than a handful of moderate Republicans who finally realize that by voting in Congress with the Tea Party (or its successor), they are not full-fledged members of the Republican Party and can exert more influence by siding with Democrats when that works for them and their constituents, but voting with Republicans when warranted. In practical terms, both House and Senate members need to be willing to switch party affiliation if necessary to avoid government shutdowns, denial of hearings on judicial appointments, and other critical matters of governance. Sure, that is a tall order for a House member with only a two-year term, but there really is no alternative. Efforts at rump politics have fallen short in the past, mainly because the rump group's agreement to agree tends to fall apart. Basically, if you have already "betrayed" your larger party by joining a rump group, what keeps you faithful to the rump group?
The best hope for a rump style success lies in the margin of the Republican majority that holds after Nov. 8th in the Senate or House. The smaller the margin, the greater the power of the individual member to exert his or her own power to shift the balance of power on important issues in that chamber. Here in New England, independence is championed as a virtue with Bernie Sanders as the most visible example. But we have had Lowell Weicker (from Republican to Independent) , Joe Lieberman (from Democrat to "Independent Democrat" after his primary loss) and Angus King (from Democrat to Independent) among others. Lincoln Chaffee glided from Republican to Independent to Democrat.
If the ruling margin in the Senate is close, each Senator who is ideologically close to the middle can exert enormous power by being flexible about party loyalty. This happened after the year 2000 election. The Senate was 50-50 with the Vice President Cheney the tie-breaking vote for Republicans after the January 20, 2001 inauguration. But in June, 2001 Sen. Jim Jeffords of Vermont switched from Republican to Independent to caucus with Democrats and hand them the majority. If Republicans are obstructionist as expected, moderate Republicans will be under pressure to do more than beg their colleagues to be reasonable - never an effective tactic with Ted Cruz, for example. Switching to the opposing party feels too much like being a turncoat, but calling yourself independent has a positive ring to it.
By way of contrast with the above examples, Scott Brown of Massachusetts, as a member for the Senate up for reelection, touted his "bipartisanship". But that was a smokescreen -- he made a show of voting with Democrats when the outcome was predetermined regardless of his vote while he voted with his Republican Party stalwarts when it mattered. Brown even made a show of standing to applaud President Obama at the State of the Union address at moments when Republicans remained sitting, which fooled no one about his independence. No surprise that his main selling point to be elected in opposition to Elizabeth Warren was to accuse her trumping up her Native American heritage.
So the independence must be real, not faked. More on this after November 8th.