Davis had a secret weapon. Robert E Lee and some other very aggressive and smart generals. The Army of the Potomac believed that Lee was unbeatable and knew every time they would come up against him, they would lose the fight.
Meade failed follow up at Gettysburg, when an extra effort could have trapped most of Lee's army on the wrong side of a river, but they were allowed to slip back into Virginia. Though badly mauled, Lee's army had managed to scrounge boots, guns and ammunition from the Federal supply dumps. If Meade had pursued Lee, he could have shortened the war by a year.
As it was, it would take a new general, a brawler like Grant to pound the Confederate forces until they were too depleted to put up any real resistance as finally happened in April 1865 at Appomattox court house when Major Gen. John Parke's command gave chase to the retreating rebel army when they retreated from Petersburg and Richmond.
Jeff Davis fled Richmond to be captured a short while later. It was Lee who surrendered the south to end the Civil War, not Davis.

the last general on the field was joe Jonston and the army of the south a week after lee he surrendered his aemy i believe to sherman
Davis attempted to escape

Yichel , I am sure that your estimate of 20-30 thousand lives saved if the war ended in 1863 is far too low .in the battles of Atlanta, Kennesaw Mt.,Resaca,Chickamauga,Cold Harbor,Petersburg,the Wilderness ,Spotsylvania,Franklin,and Nashville produced a total of 132,000 casualties , and these are only the battles that I came up with off the top of my head that happened after July 4, 1863 . I am sure that I missed quite a few . Of course these numbers are total casualties and include wounded also , if you add all of the battles that I missed and if you factor in that deaths from disease while in the field were higher throughout the war than battle deaths , the total for the additional 2 years of war has to be at least 100,000 .

As to why Davis didn't accept surrender terms in 1863 , at that time Davis's position was very similar to Ho Chi Minh's position in the Viet Nam war . He knew that it was extremely unlikely that he could win a military victory , but he was hoping to make the war so costly for the Union that they would give up fighting . Again , much like in the Viet Nam war , there was much public sentiment in the North for ending the war . In fact , the Emancipation Proclamation was a blatant political ploy by Lincoln to get the support of the rabid abolitionists in order to offset the pressure for peace from the majority of the people .Nixon didn't have an Emancipation rabbit to pull out of his sleeve , so we withdrew from Viet Nam .

Also in 1863, Davis had some hope of still gaining either British or French recognition of the CSA. With recognition, French and British ships could not be interfered with and trade of cotton and tobacco for guns and war materiel would have given the South a chance of surviving.
If the South had gained recognition from either of those two countries, any interference by the US Navy with their ships within the CSA's territorial waters would have been considered an act of war, and that is one thing that Lincoln wanted to avoid at all costs even though there were members of his cabinet who urged war with Great Britain.
The French Emperor Napoleon III had imposed Maximillian the brother of Kaiser Franz Josef of Austria-Hungary on Mexico, creating the Empire of Mexico resulting in a civil war in Mexico. There French armed forces in Mexico that could have posed a threat by allying with the CSA.
The British in Canada posed another threat in case of war with Great Britain. Even though the US Navy had grown into a potent force, it still was no match for the Royal Navy since all of the USN's resources were involved in blockading the South and chasing sea raiders around the world.

By 1863 Btish already had a nw source for cotton, any cotton they were getting from america was mostly from the north taken by union forces a few southern ships got by the blockade but only a few. Anaconda was one effective strategy. It was a forlon hope Frances relationship with the south i know nothing

The CSA government hung on until the bitter end and then fled when Lee abandoned the defenses at Petersburg and tried to slip south, perhaps hoping to join up with Johnston. The CSA leadership were fanatics grasping at straws in hope of continuing the war.
In desperation the CSA government burnt anything that could be of military value to the Yankees.
By April 1865, the infrastructure of the South was in ruins. Atlanta and other cities were burned or devastated by bombardment. Sherman's march had destroyed vast amounts of farm land. The Shenadoah Valley, one of the most productive agricultural areas in the South was in ruins.
The railway system was worn out and many rail lines had been destroyed.
Southerners had lost hundreds of millions of dollars in property when their slaves were emancipated or dispossessed of their estates by the occupying military authority through the imposition land taxes and other quasi-legal means through military imposed local governments.
It was the carpetbaggers and the roughshod handling by the military after the ware that deeply embittered the Southerners which lasts to this day.
Lincoln's death allowed the rapacious and vengeful North to persecute the South with the imposition of Reconstruction.

At that point in time, the war was still winnable by the South or maybe better described as loseable by the North.....

Had there been such an offer and had it been accepted the South would almost certainly rejoined the Union within a decade, but the resultant union would have been much different I suspect.....

The loss of Vicksburg and the Lee's escape after Gettysburg in the summer of 63 meant that even having to go on the defensive, the North had not shown it really meant to hold the South in the Union. Things were bad for the South, only a trickle of military supplies were getting through the naval blockade and the trans-Mississippi states were cut off with the Yankee control of the Mississippi. However, the southern generals were deemed to be superior to any the Yankees had heretofore fielded with the exception of Grant and Sherman in the West.
It wasn't until early 64 nearly a year after debacles of Vicksburg and Gettysburg that Grant was finally given command of the Union Army. By then it was too late for any more talking. The war entered its most bitter and deadly chapter that could only end with the complete annihilation of the Confederate government and the occupation of the southern states.

it seems that at that point moving grant east withhis intention of destroying lees army first then richmond made the diffeence i often read how lee thiygh about attempting to get into the shendoah and fight a guerrilla war that would have been a night mare. grant just kept extending and thinning Lee's line Lee must have felt ike butter being spread on too many slices of bread.