With a divided government (Congress controlled by Republicans, the presidency by a Democrat), there is basically nothing notable other than appropriations that can become law. Standalone bills with any kind of a conservative aim would be vetoed if they made it past Senate Democrats' filibusters. Congress cannot directly repeal anything (e.g., Obamacare) until there is a new president. That leaves the option of attaching legislation to spending bills. But a spending bill from the House which tries to accomplish anything would also be filibustered or vetoed. Some people advocate for Congress to allow government shutdowns in order to pass policies that could not become law on their own, but historically this fails. The administration engages in shutdown theatrics, Republicans are demonized in the mainstream media (which most people do listen to), and eventually they pass a continuing resolution.
As Eric Cantor writes:
...somewhere along the road, a number of voices on the right began demanding that the Republican Congress not only block Mr. Obama’s agenda but enact a reversal of his policies. They took to the airwaves and the Internet and pronounced that congressional Republicans could undo the president’s agenda — with him still in office, mind you — and enact into law a conservative vision for government, without compromise.Boehner and McConnell are leadership, not dictators. They represent their caucuses. They can set the tone, they can negotiate. But they still have to face a Democrat president. As Jay Cost explains:
Strangely, according to these voices, the only reason that was not occurring had nothing to do with the fact that the president was unlikely to repeal his own laws, or that under the Constitution, absent the assent of the president or two-thirds of both houses of Congress, you cannot make law. The problem was a lack of will on the part of congressional Republican leaders.
The last Republican speaker to face a president nearly so liberal was Joseph Martin, who served from 1947 to 1949. But Martin could often count on an alliance with the now-extinct faction of conservative Southern Democrats. Boehner had no such bipartisan opportunities, so he could get precious little accomplished with Obama in the Oval Office.McConnell has the added problem of filibusters. Controversial bills typically don't pass the Senate without 60 votes to end debate and the Republicans have 54. That is where bills die. They never make it to President Obama because Senate Democrats won't allow them to leave the Senate.
In the long run, though, [possible successor Kevin] McCarthy will succeed only if a Republican wins the White House next year.
Maybe he can keep the conservatives happy for the next 12 months, but without a GOP presidential victory, it will eventually be for naught.
The challenge for critics of Boehner and McConnell's is to explain exactly what they would do differently and what the result would be. Complain obnoxiously, turning off voters but ending up with the same legislative non-results? Want to repeal Obamacare or impeach the president? How are you going to get 43 out of 188 Democrat representatives and 13 out of 46 Democrat senators to vote against the leader of their party?