The white factions were on the whole as the previous post said exceptionally lukewarm about the monarchy and even pro-monarchists were unwilling to name some kind of royal figurehead for fear of alienating the numerous republican groups and sects fighting the bolsheviks.
The Romanov's were pretty much a spent force - with or without the murders and most of the family would have been very reluctant to rally round an exiled and quite frankly disgraced Nicholas.
Nicholas II had abdicated (whatever the legality of that).
Technically his brother Michael Alexandrovitch had become Emperor (or for those who dispute the abdication regent for his nephew Alexei).
Michael's manifesto had put the question of a monarchy off until a constitutional vote could be taken (it was of course forgotten when the Bolshevik's took control)
Michael left leaving until far too late and was on the point of departing for Finland - he was murdered before Nicholas II in June 1918
Many pro-monarchists preferred Grand Duke Nicholas (grandson of Nicholas I and wartime general) as Emperor and Autocrat - others supported the technical next in line Kyril Vladimirovich others Dmitri Pavlovich.
Depends which Romanov murders you want to remove on who has the best or strongest claim etc.
The family as a whole supported the right and claims of Kyril Vladimirovich (who by the 20s was the senior surviving heir male) with only Nicholas Nikolaevich and his brother objecting. The family would later split over the decision of Vladimir - Kyril's son - naming his daughter heir and insisting the other male dynasts marriages were invalid for the purpose of succession (a long-running and unpleasant battle that is still going on within the descendants of the Romanov survivors)
The murders in order:
Michael Alexandrovich (the defacto last Emperor) June 1918
The former Imperial Family - July 17 1918
Alapaevsk group - Sergei Mikhailovich, John/Ivan Constantinovich, Constantine Constantinovich, Igor Constantinovich - plus Grand Duchess Elizabeth (sister of the Empress Alexandra) and Prince Paley (morganatic son of Grand Duke Paul) - 18 July 1918.
Peter and Paul Fortress Group - 28 Jan 1919 - Grand Dukes Dimitri Constantinovich, Nicholas Mikhailovich, George Mikhailovich and Paul Alexandrovich.
The actual succession of the House of Holstein Gottorp Romanov as of the Fall of the Monarchy.
Group 1 - Descendants of Alexander III -
1) Alexei Nikolaevitch (discounting his father's abdication on his behalf)
2) Michael Alexandrovitch - Emperor according to Nicholas II's abdication murdered in June 1918)
Group 2 Descendants of Alexander II:
1) Kyril Vladimirovitch,
2) Vladimir Kyrillovitch (b1917)
3) Boris Vladimirovich
4) Andrei Vladimirovich
5) Paul Alexandrovitch (kd 1919)
6) Dmitri Pavlovich (Rasputin's killer and another oft named candidate during the civil war).
Descendants of Nicholas I
Group 3
1) Nicholas Constantinovich (d Jan 1918)
2) John/Ivan Constantinovich (murd July 1918)
3) Vsevolod Ivanovich
4) Gabriel Constantinovich
5) Constantine Constantinovich (murd july 1918)
6) Igor Constantinovich (murd july 1918)
7) George Constantinovich
8) Dmitri Constantinovich (Kd Jan 1919)
9) Nicholas Nikolaevich (war time general and oft named candidate during the civil war)
10) Peter Nikolaevich
11) Roman Petrovich
12) Nicholas Mikhailovich (murd Jan 1919)
13) George Mikhailovich (murd Jan 1919)
14) Alexander Mikhailovich
15) Andrei Alexandrovich
16) Feodor Alexandrovich
17) Nikita Alexandrovich
18) Dmitri Alexandrovich
19) Rostislav Alexandrovich
20) Vasili Alexandrovich
21) Sergei Mikhailovich (Murd July 1918)