No, not really.
The call for Rohan's aid doesn't come the same in the books as in the movies; in the movie, he's summoned by the beacon-fires of Gondor, but in the book a messenger arrives with the symbolic Red Arrow. Here's how that conversation goes (emphasis mine):
A tall man entered, and Merry choked back a cry; for a moment it seemed to him that Boromir was alive again and had returned. Then he saw that it was not so; the man was a stranger, though as like to Boromir as if he were one of his kin, tall and grey-eyed and proud. He was clad as a rider with a cloak of dark green over a coat of fine mail; on the front of his helm was wrought a small silver star. In his hand he bore a single arrow, black-feathered and barbed with steel, but the point was painted red.
He sank on one knee and presented the arrow to Théoden. 'Hail Lord of the Rohirrim, friend of Gondor!' he said. 'Hirgon I am, errand-rider of Denethor, who bring you this token of war. Gondor is in great need. Often the Rohirrim have aided us, but now the Lord Denethor asks for all your strength and all your speed; lest Gondor fall at last.'
'The Red Arrow!' said Théoden, holding it, as one who receives a summons long expected and yet dreadful when it comes. His hand trembled. 'The Red Arrow has not been seen in the Mark in all my years! Has it indeed come to that? And what does the Lord Denethor reckon that all my strength and all my speed may be?'
'That is best known to yourself, lord,' said Hirgon. 'But ere long it may well come to pass that Minas Tirith is surrounded, and unless you have the strength to break a siege of many powers, the Lord Denethor bids me say that he judges that the strong arms of the Rohirrim would be better within his walls than without.'
'But he knows that we are a people who fight rather upon horseback and in the open, and that we are also a scattered people and time is needed for the gathering of our Riders. Is it not true, Hirgon, that the Lord of Minas Tirith knows more than he sets in his message? For we are already at war, as you may have seen, and you do not find us all unprepared. Gandalf the Grey has been among us, and even now we are mustering for battle in the East.'
'What the Lord Denethor may know or guess of all these things I cannot say,' answered Hirgon. 'But indeed our case is desperate. My lord does not issue any command to you, he begs you only to remember old friendship and oaths long spoken, and for your own good to do all that you may. It is reported to us that many kings have ridden in from the East to the service of Mordor. From the North to the field of Dagorlad there is skirmish and rumour of war. In the South the Haradrim are moving, and fear has fallen on all our coastlands, so that little help will come to us thence. Make haste! For it is before the walls of Minas Tirith that the doom of our time will be decided, and if the tide be not stemmed there, then it will flow over all the fair fields of Rohan, and even in this Hold among the hills there shall be no refuge.'
'Dark tidings,' said Théoden, 'yet not all unguessed. But say to Denethor that even if Rohan itself felt no peril, still we would come to his aid. But we have suffered much loss in our battles with Saruman the traitor, and we must still think of our frontier to the north and east, as his own tidings make clear. So great a power as the Dark Lord seems now to wield might well contain us in battle before the City and yet strike with great force across the River away beyond the Gate of Kings.
'But we will speak no longer counsels of prudence. We will come. The weapontake was set for the morrow. When all is ordered we will set out.
Return of the King Book V Chapter 3: "The Muster of Rohan"
Although he's rightfully concerned for his own borders, he doesn't express any of the hesitation he does in the movie; he actually expresses quite a lot of hesitation in the movie, point-blank refusing to come to Gondor's aid at one point:
Gandalf: If the beacons of Gondor are lit, Rohan must be ready for war!
Théoden: Tell me. Why should we ride to the aid of those who did not come to ours? What do we owe Gondor?
The Return of the King (2003)
The events also come at different times. In the movie, Dunharrow is the site of the Muster of Rohan, and a stop on the road to Gondor. In the book, Théoden is already at Dunharrow when he receives the Red Arrow; he intended to pass through Dunharrow to reach his muster at Edoras.