President Obama’s displeasure with gridlock in Washington — and with the Republicans he blames for it — has been rising for months. This week it has boiled over.

From the Rose Garden to the Cabinet Room to near the Key Bridge in Georgetown, the president has signaled more than mere annoyance at the state of affairs at the halfway point of this year. His disdain for congressional Republicans has steadily increased; his disrespect for their tactics has hardened into contempt.

With immigration reform dead for this year, if not for the remainder of Obama’s presidency; with House Speaker John A. Boehner (R-Ohio) threatening to sue him for alleged misuse of presidential power; and with other important legislation stalled in the House, the president has given voice to his frustrations with a series of partisan blasts.

It culminated Tuesday with a mock dare to the speaker and his followers in the House: “So sue me!”

The president tries to mask his irritation with assurances that his door is open, his arm extended and his willingness to compromise as genuine as ever. Here’s the way he put it at a meeting with his Cabinet on Tuesday morning: “Keep in mind that my preference is always going to be to work with Congress and to actually get legislation done.”

President Obama acknowledged Monday that there is no hope for legislation overhauling the immigration system in Congress this year, and announced he will be issuing a series of executive actions to repair the situation. (The Associated Press)

Hours after those remarks, he offered an assessment of his opponents that hardly seemed designed to persuade them that he’s really prepared to work with them.

“Republicans in Congress, they’re patriots, they love their country, they love their families,” he said from the Key Bridge. “They just have a flawed theory of the economy that they can’t seem to get past. . . . That’s their worldview. I’m sure they sincerely believe it. It’s just not accurate. It does not work.”

The object of Obama’s anger Monday was the stalled immigration reform bill, which has been bottled up in the House because of divisions among Republicans. The influx of children on the U.S.-Mexico border has created a fresh immigration crisis for him to deal with. Meanwhile, he wants administration officials to draft proposals for him to act on his own to deal with the overall problem.

On Tuesday, his unhappiness was directed at the lack of progress on legislation to replenish the Highway Trust Fund, which is set to run out of money later this year. There is a bipartisan proposal in the Senate from Sens. Bob Corker (R-Tenn.) and Chris Murphy (D-Conn.) that would provide a permanent solution.

The Corker-Murphy bill calls for increasing the gasoline tax by 6 cents a gallon in each of the next two years and then indexing the tax to inflation, with offsets to keep the measure revenue-neutral. The administration has proposed a shorter-term solution, not a long-term fix. For now, nothing is moving, although the trust fund long has been supported by Republicans and Democrats.

Consensus-seeking long has been part of the president’s self-perception. He suggests he is the conciliator-in-waiting, lacking only a willing hand across the aisle. But the longer he has faced opposition from enough House Republicans to block action on a series of bills, the more he’s tried to break the gridlock by seeking to capitalize politically.

In the face of widespread disaffection toward Washington and with congressional approval ratings falling below 10 percent, the president wants to be seen as the one person trying to take action on behalf of people. What­ever he can to do to separate himself from other politicians in Washington, the better.

“We’re not always going to be able to get things through Congress, at least this Congress, the way we want to,” Obama said at his Cabinet meeting. “But we sure as heck can make sure that the folks back home know that we’re pushing their agenda.”

Obama’s goal in all this is obvious. He desperately wants to avoid seeing the Senate fall into Republican hands. The GOP needs to gain only six seats to take full control of Congress for Obama’s final two years in office. Though some of the races they hoped would materialize haven’t yet done so, there are more than enough opportunities for the Republicans to do so.

Democrats running for reelection know the most helpful thing Obama can do for them is to raise his approval ratings. But at this point he remains stuck in the low 40s. A new Quinnipiac University poll released Wednesday found that 54 percent of registered voters say the administration is not competent to run the federal government.

Given the state of the economy and the state of the world, Democrats have to wonder whether there is much Obama can do between now and November to boost those numbers.

The president is not welcome in some of the states with competitive Senate races this fall. What he can do is raise money and speak to the constituencies Democrats need to have energized in November. His advisers signaled earlier that he will be out of the White House as much as possible.

His public appearances, despite whatever comments he makes about his desire to work with Congress, have been designed to sharpen the partisan divisions, to belittle the Republicans, and to say to middle-class families and especially unmarried women that he’s with them and the Republicans aren’t.

Obama said Tuesday that the people who can change the status quo are the voters. That is reminiscent of his 2012 campaign, when for a time he said it was up to the voters to break the tie in Washington. Many voters didn’t really believe that then, and the election of 2012 didn’t change much in Washington. Will a repeat performance work any better this time?