Donald Trump reached out to the GOP establishment on March 8. Does that mean he's ready to make peace with some of his toughest Republican critics? (Peter Stevenson/The Washington Post)

The Republican presidential campaign has entered what could be the most critical week of the primary season, with the party elites almost out of time to deny the GOP nomination to New York billionaire Donald Trump short of a potentially bloody fight at the national convention in July.

Trump’s easy victories in Michigan and Mississippi demonstrated appeal from the Deep South to the industrial Midwest that continued his impressive winning string and added to his lead in delegates. While not unexpected, his margins — especially in Michigan — were bigger than his rivals had hoped they would be.

So far his opponents have won only scattered victories by comparison but nothing that amounts to critical mass in the stop-Trump movement. Sen. Ted Cruz of Texas has done better than Ohio Gov. John Kasich or Sen. Marco Rubio of Florida, but none has yet emerged as strong enough alone to stop him, though Cruz may be best positioned to fill that role.

After Tuesday, the stop-Trump movement’s short-term strategy rests on two candidates and two states: Kasich in Ohio and Rubio in Florida. But Tuesday showed there are no sure things ahead.

Kasich has yet to win a contest and was looking for a clear and strong finish in Michigan to give him a boost. Instead he finished well behind Trump in Michigan and was in a fight with Cruz for second.

Tracking the race to the Republican nomination

Meanwhile, Tuesday continued Rubio’s sudden and rapid descent. A few weeks ago, he was the establishment favorite, the man seen as best positioned to challenge Trump through the spring. Today he is a battered candidate.

In Michigan, Rubio was scratching to reach double digits in the popular vote. That was impressive, compared with his showing in Mississippi, where he was mired in single digits, along with Kasich. In that state, as Trump romped, Cruz lapped the other two and finished second.

It’s not out of the question that Kasich and Rubio could win their home states next week, but after what happened Tuesday, they will face heavy competition, and not just from Trump. Cruz also sees vulnerabilities in his rivals and will seek to exploit them.

All of this comes despite signs that Trump, who has dominated the Republican race and defined the 2016 cycle for months with his bombastic rhetoric and unorthodox campaign style, has begun to show weakness and limits. As opposition to his candidacy has mounted inside the Republican Party, the lines have hardened around his candidacy, pro and con.

In national polls, his margin is narrower than it once was. Nearly half of all Republicans say they would not be satisfied if he becomes the nominee, according to the latest Washington Post-ABC News poll. His favorability rating among Republicans, while still net positive, has declined over the past few months. And in one-on-one tests against Cruz and Rubio, he loses, according to the same poll.

Had this begun to happen two months ago, Trump might be far more vulnerable than he looks today — or so some Republicans would like to think. But even that is open to question.

The party elites unloaded on Trump over the past week, led by 2012 nominee Mitt Romney, who portrayed Trump as unfit to be president and a lousy businessman. Wealthy donors offered up millions of dollars to anti-Trump super PACs for attack ads.

None of it seemed to have much effect Tuesday, although the focus of these efforts is targeted more on next week’s results.

Up to now, according to the Republican rules, almost all states so far have awarded delegates on a proportional basis. But that begins to change next week in a way designed to help a front-runner and hinder those behind.

Starting next week, many states will award delegates on a winner-take-all basis. Trump doesn’t have to win half the vote to get all the delegates in upcoming states; he can do so with the kind of percentages he has rolled up so far.

Trump still remains far short of the 1,237 delegates needed to win the nomination. Losses in Ohio and Florida would block him from 165 delegates. But winning either or both would cripple efforts to prevent him from becoming the nominee.

The possibility of a convention fight still looms. As of Tuesday night, more than 1,000 delegates have been awarded. After next Tuesday, that jumps to almost 1,500 — of 2,472 total. Trump still could be denied a first-ballot victory, but which among his rivals would be close enough to claim the right to be the alternative?

Rubio’s prospects have faded dramatically. He needs a stunning turnaround, beginning in Florida and then elsewhere. Kasich could win Ohio. If he were to do that, other Midwestern states could be fertile territory, but after what happened Tuesday in Michigan, he could not count on them.

Cruz and his advisers long have believed that a head-to-head race would favor him over Trump. But a look at the calendar after next week raises questions about his path. So far, other than his victory in Texas, he has had trouble demonstrating that he has support that is significantly broader than his evangelical base.

Right now, Cruz has done less well overall than former Pennsylvania senator Rick Santorum, who had a similar base of support, did in 2012. Both won the Iowa caucuses. Santorum went on to win 10 more states. Of the seven that have voted already this year, Cruz has won two, Rubio one and Trump four.

Cruz can win caucus states and some smaller contests. His real test will come in states such as Wisconsin, New York, Connecticut, New Jersey and California.

Trump is still an unusual front-runner — polarizing in his own party and with vulnerabilities that become more apparent week by week. Were he to falter next week or after that, the anti-Trump forces will be emboldened to continue their attacks. Their hope remains to keep him short of a majority and then upend him in Cleveland in July. But they needed a better result on Tuesday than they got. Trump remains in control of the race.