Here's a list of categories to determine where some of them stand.
Some party members who were lukewarm on Trump ran away from the nominee shortly after the comments came to light.
Idaho Sen. Mike Crapo, who is up for reelection, on Saturday became the first sitting Republican senator to back away from Trump following the incendiary comments. "This is not a decision that I have reached lightly, but his pattern of behavior has left me no choice. His repeated actions and comments toward women have been disrespectful, profane and demeaning."
Soon after Crapo's announcement, Ayotte, who is also up for reelection, also said she would not vote for Trump.
In August, Ayotte had said she would vote for Trump but not formally endorse him.
She said Saturday she will instead be writing in Pence on Election Day.
Arizona Sen. and former Republican Party nominee John McCain, who is up for reelection, said Trump's behavior "make it impossible to continue to offer even conditional support for his candidacy."
Former Secretary of State Condoleezza Rice declared "Enough!"
in a Facebook post, adding, "Donald Trump should not be President. He should withdraw."
Alaska Sen. Lisa Murkowski said
Trump has "forfeited the right to be our party's nominee."
Maine Sen. Susan Collins, who had said after the Republican National Convention that she would not support Trump, reiterated her stance that she is "still not voting for Hillary, and still plans to write in someone."
Alabama's Republican governor, Robert Bentley, said in a statement he
"cannot and will not vote for Donald Trump."
In the House, Alabama Rep. Martha Roby said Saturday she will not vote for him and that he should step aside. Roby is from a safe district and is often featuring in GOP family friendly initiatives.
Ohio Sen. Rob Portman issued a statement Saturday night in which he pulled his support and said he would instead vote for Pence.
Friday night, House Oversight Committee Chairman Jason Chaffetz became the first sitting Republican congressman
to pull his support for Trump in the wake of the 2005 video, which was surfaced by The Washington Post earlier in the day.
Utah Gov. Gary Herbert on Friday became the first sitting Republican governor to withdraw his vote over the comments, which he called
"offensive and despicable."
Ignoring Trump going forward
House Speaker Paul Ryan told Republicans Monday he will no longer defend Trump -- and will instead use the next 29 days to focus on preserving his party's hold on Congress. "The speaker is going to spend the next month focused entirely on protecting our congressional majorities," Ryan's spokeswoman, AshLee Strong, said in a statement.
Rep. Mike Bishop, R-Michigan, said in a statement Monday that Trump was neither his first nor second choice during the Republican primary, and going forward would stop answering questions about Trump. He said in the statement: "Our families deserve a campaign that is focused on the issues, something our 2016 discussions are solely lacking this close to Election Day."
Sticking by Trump
Many Republicans, beginning on Friday night and into Saturday, slammed Trump over the remarks but either said he was preferable over Democrat Hillary Clinton or didn't address their support for him at all.
Pence said he does not "condone" Trump's remarks and "cannot defend them" but is "grateful that he has expressed remorse and apologized."
Texas Sen. John Cornyn, the No. 2 Senate Republican, tweeted he is "disgusted by Mr Trump's words" and is "profoundly disappointed by the race to the bottom this presidential campaign has become."
House Majority Leader Kevin McCarthy said "there is absolutely no place" for Trump's language in American society and that he "must" make a "full and unqualified apology."
Top Trump surrogate Ben Carson said "in no way do I condone Trump's behavior" but said he was "fairly certain"
progressives knew about Trump's 2005 remarks but waited until now to damage his candidacy.
Louisiana Rep. Steve Scalise said "women deserve to be treated with respect. Period," and that Trump should make "a direct apology."
Iowa Sen. Joni Ernst, a rising star in the party, called
Trump's remarks "lewd and insulting."
Kentucky Sen. Rand Paul called Trump's comments "offensive and unacceptable" -- but a spokesman didn't respond when asked if Paul was still going to vote for Trump.
Pence for president
Several Republicans said Pence should lead the ticket.
South Dakota Sen. John Thune, the No. 3 Senate Republican and a member of Majority Leader Mitch McConnell's inner circle, wants Trump to "withdraw," saying, "Mike Pence should be our nominee effective immediately."
Nevada Rep. Joe Heck -- who is running for Democratic leader Harry Reid's Senate seat -- said Trump should "step down and allow Republicans the opportunity to elect someone who will provide us with the strong leadership so desperately needed."
Rep. Barbara Comstock, R-Virginia, said Trump's comments were "disgusting, vile and disqualifying" and called for Pence "or another appropriate nominee" to replace him.
Rep. Ann Wagner, R-Missouri, wrote, "I withdraw my endorsement and call for Governor Pence to take the lead so we can defeat Hillary Clinton."
Colorado Sen. Cory Gardner said if Trump wishes to defeat Clinton, he must "step aside," adding, "I will not vote for Donald Trump."
Utah Sen. Mike Lee posted a Facebook video asking Trump to step down: "Your conduct, sir, is the distraction."
Illinois Sen. Mark Kirk tweeted that Trump should drop out and that Republican Party leaders should engage rules for an emergency replacement.
South Dakota Gov. Dennis Daugaard is backing Pence tweeting that "enough is enough" and "this election is too important" to keep backing Trump.
Dan Sullivan, Alaska's junior Republican senator, called
on Trump to step aside for Pence as the billionaire "can't lead on critical issue of ending domestic violence and sexual assault."
"It would be wise for him to step aside and allow Mike Pence to serve as our party's nominee," Nebraska Sen. Deb Fischer tweeted.
A special category for Ted Cruz
First Ted Cruz made a big show of not endorsing Donald Trump at the Republican National Convention because Trump had insulted his wife and suggested his father helped kill JFK (not true). Then, Ted Cruz ultimately endorsed Trump, although not wholeheartedly. Now, a source close to Cruz confirms he is considering withdrawing that endorsement. But he has not yet.
#NeverTrump digs in
Republicans who have opposed Trump for months were only too happy to once again declare their opposition to him.
Former presidential candidate Jeb Bush said that "no apology can excuse away Donald Trump's reprehensible comments degrading women."
Ohio Gov. John Kasich on Saturday made it clear he would not vote for Trump, adding, "Nothing that has happened in the last 48 hours is surprising to me or many others."
Nebraska Sen. Ben Sasse tweeted, "character matters" and said Trump should "make an honorable move" and "step aside & let Mike Pence try."
Former California Gov. Arnold Schwarzenegger -- who campaigned with Kasich
during the primaries -- said Saturday this election will be the first presidential contest where he won't vote for the GOP candidate.
And former Hewlett-Packard CEO Carly Fiorina -- a Trump rival during the primary season -- issued a statement
backing Pence and saying, "Donald Trump does not represent me or my party."