But the question isn't about the meaning of point blank. It's eminently possible that Booth manages to bungle his assassination. Lincoln moves slightly and is wounded.
Taking things from there, it's clear that Lincoln wouldn't have allowed the Radical Republicans to have a field day. It's equally clear, though, that the South will begin trying to restrict black voting rights and the like. Where Lincoln would draw the line is unclear. He may support something like the 14th Amendment (or rather just it's first clause) because it overturned the Dred Scott decision. In any event, he will make a very certain mark on how the Federal government deals with / enforces civil rights in the States.
Lincoln's Reconstruction may permit a certain amount of disenfranchisement and the like but push the Freedman's Bureau (which was created in March 1865). If Reconstruction is solely economic and doesn't entail the forced political changes of 1866-1868, then the backlash against it will be very different. There will still be a backlash, motivated by the sheer amount of money being spent. However, it may not be as successful. Poor Southern whites--and many Southern Unionists were such folk (though not all poor southern whites were unionists, not by any stretch of imagination)--may benefit from the Bureau as well, which was technically the Bureau of Refugees, Freedmen, and Abandoned Lands, so it could cover them as well. If Lincoln pushes this version of Reconstruction, it is essentially a version of the New Deal some 80 years early.
A big question is of course whether Lincoln runs for re-election in 1868. There are strong reasons for him not to: Firstly, there is the precedent of Washington. Secondly, there's the immense toll being president had wrought. However, Lincoln's "only" 59 in 1868 and certainly could have lived for another decade or so. By 1868 the Republican Party -- and recall that in 1864 Lincoln and formally run as a member of the Union Party -- is increasingly split between Radicals and Unionists/Moderates/Lincolnites. I tend to think Lincoln will be strong enough to ensure his dominance over the Radicals.
There are two potential candidates to succeed Lincoln: US Grant and William Seward. Seward is IMO the last man standing of the rivals whom Lincoln beat in 1860 for the GOP nomination. He probably agrees with much of Lincoln's program, but his primary focus has been foreign affairs. US Grant has a great profile, but not much of a political reputation. OTL refusing Johnson's appointment to Sec War when Johnson removed Edwin Stanton (and thus violated the Tenure of Office Act and invited impeachment) endeared Grant to the Radical Republicans. He certainly supported a vigorous Reconstruction policy. Grant was also fairly young, 46, and was when elected the youngest man then elected to the Presidency. I tend to think Seward may be a better bet than Grant, though Grant may make a nice VP.
The next issues is whether Lincoln's Reconstruction creates the same kind of politics that undermined OTL Reconstruction. TTL won't create animosity through military rule in 1866. Economic support through the Freedman's Bureau may well win GOP votes in the South and dent the rise of sharecropping as a replacement of slavery. However, it will still invite the attack taken by the Liberal Republicans of OTL, that it was too expensive to maintain for long. However, I would argue that a Reconstruction that focused more on economic rehabilitation than on forced political reform would be more successful in the long run (essentially Booker T. Washington's thesis). If the Freedman's Bureau is abolished or greatly curtailed by the mid 1870s, the economy of the South (and for black workers) may be sufficiently altered that a viable black middle class can emerge to advocate for greater political rights later on during an alt-Progressive era. Additionally, the precedent of an Economic Reconstruction will greatly impact the nature of Populist proposals later in the 1880s and 1890s, since by that time the Grange movement began to support interventionism and may advocate for similar programs to be reinstated. This of course may tie the Populists and the Progressives more closely together than occurred OTL.